GIFT  OF 


THE  N.  W.  HARRIS    LECTURES 
FOR    1913 


is:  ]Lectur** 


were  founded  in  1906  through  the  generosity  of  Mr. 
Norman  Wait  Harris  of  Chicago,  and  are  to  be  given 
annually.  The  purpose  of  the  lecture  foundation  is, 
as  expressed  by  the  donor,  "to  stimulate  scientific 
research  of  the  highest  type  and  to  bring  the  results 
of  such  research  before  the  students  and  friends  of 
Northwestern  University,  and  through  them  to  the 
world.  By  the  term  '  scientific  research  '  is  meant 
scholarly  investigation  into  any  department  of  human 
thought  or  effort  without  limitation  to  research  in  the 
so-called  natural  sciences,  but  with  a  desire  that  such 
investigation  should  be  extended  to  cover  the  whole 
field  of  human  knowledge." 


THE  CONSTITUTION  OF 
MATTER 


BY 


JOSEPH  S.  AMES,  PH.D. 

PROFESSOR    OF    PHYSICS 

AND    DIRECTOR    OF    THE    PHYSICAL    LABORATORY 
JOHNS    HOPKINS    UNIVERSITY 


BOSTON   AND   NEW  YORK 
IIOUGHTON  MIFFLIN  COMPANY 

retftf  Camb  i&ge 
1913 


W7I 


COPYRIGHT,   1913,   BY  JOSEPH  S.   AMES 
ALL   RIGHTS   RESERVED 

Published  November  79/5 


PREFACE 

THE  lectures  which  form  the  body  of  this  book 
were  delivered  at  Northwestern  University, 
Evanston,  Illinois,  in  the  month  of  February, 
1913,  for  The  Norman  W.  Harris  Lectures  of 
this  year.  The  fact  that  they  were  actual  lec- 
tures accounts  for  the  form  in  which  the  text 
is  given ;  and  the  further  fact  that  the  audi- 
ence for  whom  they  were  prepared  was  com- 
posed, for  a  large  part,  of  people  unfamiliar 
with  both  the  facts  and  the  methods  of  science 
must  be  accepted  as  the  justification  for  the 
treatment  of  the  subject. 

Few  tasks  are  as  difficult  as  that  of  convey- 
ing to  a  general  audience  a  true  impression 
of  the  results  of  scientific  inquiry.  One  must 
avoid  the  Scylla  of  too  great  certainty  and 
also  the  Charybdis  of  too  great  uncertainty. 
Even  the  proper  words  to  use  are  a  matter  of 
doubt ;  and  the  difficulty  is  not  lightened  by 
the  fact  that,  through  the  daily  press  and  the 


273621 


vi  PREFACE 

popular  magazines,  many  of  the  discoveries  of 
science  have  been  given  exposition  — in  many 
cases,  by  people  entirely  ignorant  of  the  sub- 
ject. 

The  plan  adopted,  after  most  serious  consid- 
eration, was  to  accept  the  general  theory  of 
molecules  and  atoms  as  proposed  by  Sir  J.  J, 
Thomson  and  the  properties  of  electrons  as 
deduced  by  H.  A.  Lorentz,  and  to  attempt  to 
explain  how  from  these  one  may  deduce  the 
general  and  even  specific  properties  of  matter. 
This  method  obviously  is  one  suited  only  for 
a  general  audience ;  and  even  there  it  has  its 
dangers.  One  is  liable  to  produce  the  impres- 
sion that  our  theories  are  verified,  whereas  they 
are  but  hypotheses  still;  but  this  is  better, 
perhaps,  than  to  leave  the  conviction  that  noth- 
ing is  certain.  It  is  difficult  to  make  any  body 
of  listeners,  however  great  their  general  intel- 
ligence, realize  that  in  the  end  the  great  pur- 
pose of  scientific  investigation  is  the  pursuit  of 
Truth,  the  attainment  of  knowledge.  Hypoth- 
eses rise  and  fall ;  the  facts  of  experiment 
remain. 


PREFACE  vii 

The  temptation  is  great  to  stop  here  and 
there  and  emphasize  what  is  not  known,  what 
is  not  proved;  and  the  real  usefulness  of  the 
lectures  is  lessened  of  course  by  the  fact  that 
this  was  done  so  rarely.  However  successful  the 
attempt  has  been,  the  main  purpose  of  the  lec- 
tures was  to  make  clear  to  a  body  of  people, 
not  students  of  physics,  some  of  the  results  of 
investigators  in  unifying  our  knowledge  of 
the  world  around  us. 


CONTENTS 

I.  GENERAL  PROPERTIES  OP  MATTER;  MASS     .  1 

Introduction;  concept  of  matter      ....  1 
Properties  of  matter  included  in  mechanics; 

mass,  weight,  elasticity,  etc 4 

The  aether  and  radiant  energy 27 

Molecules  and  atoms;  the  periodic  system    .  36 

Corpuscles 44 

II.  CORPUSCLES  AND  ATOMS;  ELECTRICAL  MASS  .  51 
Electrification;  energy  of  charges  at  rest  and 

in  motion 53 

Radiant  energy 62 

Mass  of  an  electric  charge 63 

Electrical  mass 64 

Experimental  facts  concerning  corpuscles     .  78 

IH.  RADIO-ACTIVITY;  GRAVITATION 90 

Radio-activity;  theory  of  successive  transfor- 
mations     92 

Gravitation;  Newton's  law     ......    99 

Theories  of  gravitation 100 

Galileo's  conception  of  mass  and  weight  .     .107 

IV.  RADIATION;     FORMATION     OF     MOLECULES; 

ELASTICITY 130 

Radiation;  production,  propagation  and  ab- 
sorption    132 


x  CONTENTS 

Formation  of  molecules;  valency      ....  149 
Elasticity;  viscosity;  etc 161 

V.  PROPERTIES  OF  METALS;  THERMIONICS;  MAG- 
NETISM      169 

Conductors  and  non-conductors 171 

Heat-conductors;  electric  conduction    .     .     .  184 
Thermionics;  photo-electric  effect     .     .     .     .187 

Reflection  and  absorption 194 

Magnetism;  the  magneton 197 

VI.  MODELS  OF  ATOMS;  CONCLUSIONS     ....  200 
Summary  of  explanation  of   mass,  weight, 

radiation,  etc 200 

J.  J.  Thomson's  model  of  an  atom  ....  201 

Other  models 205 

Fundamental  concepts  of  nature;  their  de- 
velopment      219 

Conclusion 236 

INDEX  .  .  239 


THE  CONSTITUTION  OF  MATTER 


THE  CONSTITUTION  OF 
MATTER 


GENERAL  PROPERTIES  OF  MATTER;  MASS 

IN  beginning  a  course  of  lectures  upon  any 
subject  connected  with  physical  science,  it  is 
necessary  to  devote  some  time  to  fundamen- 
tal ideas  and  definitions.  This  is  specially  true 
in  dealing  with  the  "  Constitution  of  Matter/' 
the  subject  of  this  course,  involving  as  it  does 
knowledge  of  the  subjects  of  heat,  light,  and 
electricity  in  addition  to  that  of  the  familiar 
properties  of  matter. 

We  must  understand  what  is  meant  by  the 
word  "matter";  we  must  describe  its  proper- 
ties as  revealed  by  experiments  ;  and  then  we 
shall  be  ready  to  discuss  the  theories  which 
aim  to  correlate  these  properties. 

The  method  which  has  been  followed  in  the 
study  of  this  particular  problem  is  the  same  as 
is  used  in  any  investigation  in  science ;  and, 


.  'CONSTITUTION  OF  MATTER 

although  it  may  be  clear  to  the  larger  part  of 
this  audience,  it  is  of  such  importance  that  I 
must  call  your  attention  to  its  essential  steps. 
All  of  us  have  certain  sense-organs  which, 
when  stimulated,  give  rise  to  definite  sensa- 
tions :  these  have  been  called  our  "  gates  to 
knowledge."  It  is  thus  that  we  first  learn 
about  the  world  of  nature  around  us.  The 
process  is  very  slow,  as  any  one  knows  who 
has  observed  a  child  striving  to  connect  its 
sensations  of  sight  and  touch,  and  noted  how 
slowly  it  learns  to  trace  a  contour  with  its  fin- 
ger. At  first  we  attribute  the  cause  of  our  va- 
rious sensations  to  certain  definite  geometri- 
cal figures :  thus  we  can  see  a  stone  or  a  block 
of  wood ;  if  we  put  our  fingers  on  it,  we  can 
trace  its  surface ;  if  we  hold  it  in  our  hands 
we  are  conscious  of  a  pressure,  etc.  We  predi- 
cate the  existence  of  something  occupying  this 
figure,  bounded  by  this  surface,  and  call  it 
"  matter."  The  fact  that,  when  we  hold  a  stone 
in  our  hands,  we  experience  a  pressure  is  said 
to  be  due  to  a  "  property"  of  matter.  By  means 
of  our  various  senses  we  learn  to  attribute 


PROPERTIES  OF  MATTER  5 

many  properties  to  the  stone  or  the  block 
of  wood;  and  the  early  history  of  science  is 
simply  an  enumeration  of  these  properties.  We 
perform  simple  experiments  ourselves  every 
day  we  live,  and  we  soon  learn  to  believe  that, 
if  we  can  repeat  identically  any  given  set  of 
conditions,  the  same  event  will  follow,  regard- 
less of  the  time  or  place.  Such  a  belief  is  in 
reality  the  first  great  principle  of  science. 
Through  our  senses  also  we  observe  phenomena 
which  occur  at  a  distance  from  ourselves,  such 
as  the  motions  of  the  planets,  the  flashes  of 
lightning,  all  of  which  go  to  make  complete 
our  mental  picture  of  nature. 

It  was  very  soon  evident  in  the  progress  of 
science  that  many  phenomena,  many  proper- 
ties of  matter,  were  connected ;  so  that,  grant- 
ing one,  another  would  follow  as  a  logical  con- 
sequence ;  and  the  recognition  of  this  fact  was 
a  most  important  step.  Thus,  Newton  showed 
that  the  tidal  motion  of  the  oceans,  the  revo- 
lution of  the  moon  around  the  earth,  and  the 
apple  falling  from  its  tree  were  all  illustrations 
of  one  and  the  same  principle.  Similarly,  all 


6  THE  CONSTITUTION  OF  MATTER 

investigators  in  the  field  of  science,  all  phi- 
losophers, are  seeking  to  prove  the  interde- 
pendence of  natural  phenomena  of  every  kind. 
Each  year  sees  us  able  to  reduce  in  number 
the  statements  required  to  describe  these  ;  and 
when  we  say  "  we  explain  "  one,  all  that  is 
meant  is  that  we  are  able  to  show  that  it  fol- 
lows logically  from  our  previous  knowledge. 

Before,  however,  we  can  speak  of  knowledge 
of  a  phenomenon,  we  must  be  able  to  describe 
it  in  precise  language.  Thus,  we  observe  that 
all  bodies  heavier  than  air  fall  towards  the 
earth  if  they  are  free  to  drop ;  further,  we  ob- 
serve that  all  bodies,  a  feather  or  a  leaden 
bullet,  will  fall  side  by  side  in  a  space  from 
which  the  air  has  been  exhausted  by  an  air- 
pump;  but  our  knowledge  of  falling  bodies  is 
not  complete  until  we  know  the  time  required 
by  a  body  to  fall  through  any  known  portion 
of  its  path;  we  must  be  able  to  give  numbers 
to  each  element  of  the  motion.  Here  is  where 
a  difficulty  enters :  what  features  of  a  phenome- 
non shall  we  regard  as  elementary?  That  is, 
what  features  are  so  simple  that  they  do  not 


FUNDAMENTAL  PROPERTIES  7 

admit  explanation  in  simpler  language?  We 
may  begin  by  assuming,  as  did  Newton,  that 
our  idea  of  duration  of  time  and  of  space  ex- 
tension, such  as  length,  area,  and  volume,  are 
intuitive  and  that  our  ordinary  methods  of 
giving  numbers  by  clocks  and  rules  are  satis- 
factory; but  which  properties  of  matter  shall 
we  choose  as  fundamental?  and  in  case  the 
phenomenon  is  one  involving  electrical,  mag- 
netic, thermal,  luminous,  or  other  effects,  what 
steps  shall  we  take?  The  progress  of  science 
has  been  most  gradual.  At  first  as  many  of 
the  ideas  were  considered  elementary  as  was 
thought  convenient,  provided  only  that  nu- 
merical values  could  be  given  them;  then,  in 
course  of  time,  by  a  process  of  making  hypothe- 
ses and  testing  them  by  further  experiments 
and  observations,  it  was  proved  that  some  of 
these  preliminary  elementary  quantities  were 
connected;  so  that  at  the  present  time  there 
are  required  for  the  expression  of  our  descrip- 
tion of  natural  phenomena  comparatively  few 
quantities.  What  these  are  will  appear  in  the 
course  of  these  lectures. 


8  THE  CONSTITUTION  OF  MATTER 

Let  me  repeat  in  a  summary  the  essentials  of 
what  has  been  called  "the  scientific  method." 
A  phenomenon  is  observed  through  our  senses; 
we  investigate  the  conditions  under  which  it 
occurs ;  we  give  numerical  values  to  all  the 
quantities  concerned  so  as  to  describe  it  in 
mathematical  language;  then,  by  a  compari- 
son of  this  with  other  phenomena,  we  attempt 
to  discover  some  few  simple  mathematical  state- 
ments which,  if  true,  involve  as  logical  conse- 
quences those  describing  all  the  observations 
made.  These  simple  statements  are  called  the 
"  laws  of  nature  " ;  and  the  quantities  involved 
in  them  are  called  the  "fundamental  quanti- 
ties "  of  matter.  It  must  be  remembered  that 
these  last  may  deserve  their  name  "funda- 
mental" for  a  brief  season  only;  because,  as 
observations  continue,  we  may  find  that  two 
or  more  of  them  are  so  related  that  they  may 
be  expressed  in  terms  of  the  same  quantity. 

Each  of  our  senses  introduces  us  to  a  certain 
set  of  phenomena;  and  in  many  cases  we  can 
by  proper  means  include  these  in  organized 
science.  Thus,  we  have  a  temperature-sense 


FUNDAMENTAL  PROPERTIES  9 

by  means  of  which  we  recognize  that  bodies 
differ  in  "  hotness  " ;  some  we  call "  hot/'  others 
"cold."  By  means  of  our  senses  alone  we  can 
do  little  more  than  this;  but  if  we  subject  a 
piece  of  ordinary  matter  to  the  conditions  to 
which  we  give  the  names  hot  or  cold,  e.g.,  hold 
it  near  a  flame,  or  put  it  on  a  block  of  ice,  we 
may  observe  that  many  of  its  properties,  such 
as  its  size,  change ;  these  changes  we  can  meas- 
ure. Further,  we  can  determine  the  exact  con- 
ditions which  cause  the  states  we  call  hot  or 
cold ;  and  thus  a  field  of  scientific  investigation 
is  opened. 

Another  sense  which  we  all  have  is  one  called 
the  "  muscle-sense  "  ;  by  it  we  are  conscious  of 
exerting  a  force,  producing  an  effort.  It  may 
be  stimulated  in  various  ways.  Thus,  if  one 
stops  or  throws  a  ball,  there  is  a  definite  sen- 
sation, or,  in  fact,  if  we  alter  the  motion  of 
any  body.  By  means  of  our  senses  alone  we 
cannot  give  a  number  to  the  sensation;  but 
we  can  recognize  differences  in  its  intensity. 
If  the  same  body  is  given  in  turn  first  a  great 
velocity  and  then  a  less  one,  the  sensation  in 


10          THE  CONSTITUTION  OF  MATTER 

the  former  case  is  more  intense;  or,  if  two 
different  bodies  are  given  the  same  speed,  e.g., 
a  tennis-ball  and  a  baseball,  the  sensation  in 
the  latter  case  is  the  more  intense;  i.e.,  for  a 
given  change  in  motion  intensity  of  sensation 
is  associated  with  a  dense  body.  There  is  thus 
a  property  of  matter  which  becomes  apparent 
to  our  muscle-sense  when  the  velocity  of  a  body 
is  changed;  and  in  this  connection  we  speak 
of  its  "  inertia."  The  proper  numerical  value 
to  be  attached  to  this  will  be  discussed  shortly. 
Again,  if  one  holds  a  body  in  the  hand  or 
supports  a  load  on  the  back,  one  is  conscious 
of  a  definite  sensation  through  the  muscle- 
sense;  and  again  there  are  differences  in  the 
sensation  depending  upon  the  nature  of  the 
load;  a  box  full  of  sand  produces  a  more  in- 
tense sensation  than  the  same  box  would  if 
empty.  Thus  we  speak  of  a  body  as  being 
"  heavy  "or  "  light."  Here  we  have  another 
property  of  matter,  called  its  "weight,"  which 
at  first  sight  has  no  connection  with  the  pre- 
vious one,  inasmuch  as  this  property  depends 
upon  the  presence  of  the  earth. 


FUNDAMENTAL  PROPERTIES  11 

Again,  if  a  rod  held  in  the  hands  is  twisted 
or  bent,  the  same  muscle-sense  is  stimulated, 
and  by  means  of  it  certain  definite  properties 
of  matter  may  be  investigated,  such  as  "  elas- 
ticity," "  ductility,"  etc. 

These  properties  of  matter  form  the  basis  of 
the  science  called  mechanics;  and  each  must 
be  studied  in  detail,  for  any  theory  of  the  con- 
stitution of  matter  must  have  in  it  the  possi- 
bility of  explaining  these  properties,  as  well 
as  others  to  be  described  presently. 

In  order  to  study  these  properties  of  matter, 
some  method  must  be  devised  for  their  inves- 
tigation which  is  independent  of  our  muscle- 
senses  ;  these  last  simply  call  attention  to  the 
phenomena  and  note  differences  in  intensity; 
by  means  of  them  we  could  never  assign  nu- 
merical quantities.  We  can  tell  fairly  well  if 
one  body  has  the  same  weight  as  another;  but 
there  is  no  certainty  in  our  minds  as  to  exact 
equality.  One  simple  way  of  securing  by  ex- 
ternal means  the  effects  which  I  have  described 
in  connection  with  our  muscles  is  to  use  a 
spiral  coiled  spring :  if  such  a  spring  is  com- 


12  THE  CONSTITUTION  OF  MATTER 

pressed  and  then  allowed  to  expand,  it  will 
give  velocity  to  a  ball,  as  in  a  toy  gun ;  if  a  body 
is  placed  on  top  of  such  a  spring,  it  will  be 
compressed  and  finally  come  to  rest  support- 
ing the  body ;  by  means  of  compressed  springs 
we  may  easily  imagine  a  body  distorted  and 
bent.  The  use  of  a  compressed  spring  is  not, 
however,  a  particularly  simple  phenomenon; 
for  its  effect  depends  upon  the  material  of  the 
spring,  its  temperature,  etc. ;  and  further  we 
cannot  see  what  is  going  on  inside  the  material 
of  the  spring. 

If  we  demand  the  simplest  way  in  which 
the  motion  of  a  body  may  be  changed,  it  will 
be  seen  to  be  by  allowing  another  body  to 
impinge  on  it ;  this  is  illustrated  by  the  game 
of  billiards,  provided  we  assume  that  the  table 
itself  is  horizontal  and  has  no  action  on  the 
velocity.  Here  we  have  the  exceedingly  ele- 
mentary idea  of  two  bodies,  having  definite 
motions,  impinging,  and  then  having  different 
motions ;  the  motion  of  each  body  is  altered 
by  the  action  of  the  other.  This  particular 
phenomenon  was  studied  by  Wallis,  Sir  Chris- 


MASS  13 

topher  Wren,  Christian  Huyghens,  and  Sir 
Isaac  Newton,  at  about  the  same  time.  Their 
method  was  to  suspend  two  heavy  bodies,  such 
as  two  lead  or  ivory  balls,  hanging  them  from 
long  threads  of  the  same  length ;  to  draw  the 
bodies  sidewise,  release  them,  and  allow  them 
to  impinge  when  both  were  at  their  lowest 
points;  and  to  observe  the  velocities  before 
and  after  impact.  This  measurement  of  veloc- 
ity is  not  difficult,  because,  as  Galileo  was 
the  first  to  prove,  if  a  body  is  swinging  like 
a  pendulum  under  the  action  of  gravity,  its 
velocity  at  the  lowest  point  of  its  swing  is 
proportional  to  the  chord  of  the  arc  of  the 
circle  through  which  it  has  fallen,  and,  if  such 
a  suspended  body  is  given  a  certain  sidewise 
velocity  when  it  is  hanging  at  rest,  it  will  rise 
through  an  arc,  the  chord  of  which  is  propor- 
tional to  this  velocity. 

The  important  conclusion  drawn  by  Newton 
from  these  observations  was  that  using  the 
same  two  bodies,  the  ratio  of  their  changes 
in  velocity  due  to  impact  is  always  the  same, 
regardless  of  the  length  of  the  suspending 


14          THE  CONSTITUTION  OF  MATTER 

threads  or  the  arcs  through  which  they  fall. 
(Of  course,  in  calculating  the  change  in  veloc- 
ity the  observers  were  careful  to  measure  the 
velocities  of  motion  always  in  the  same  direc- 
tion, e.g.,  towards  the  right;  so,  if  it  is  said 
that  a  velocity  is  increased,  it  is  meant  that 
the  velocity  towards  the  right  is  increased, 
etc.)  If  the  two  bodies  are  of  the  same  ma- 
terial, e.g.,  both  made  of  ivory,  the  larger 
one  has  the  less  change  in  its  motion  ;  and  the 
same  is  true  in  all  cases  of  the  body  which  has 
in  it  what  we  may  call  the  greater  "  quantity 
of  matter."  It  was  noted,  further,  that  these 
changes  in  velocity  were  always  opposite  in 
direction  for  the  two  bodies;  i.e.,  using  most 
general  language,  if  one  body  is  given  a  push 
to  the  right  as  the  result  of  the  impact,  the 
other  receives  a  push  to  the  left. 

The  fact  of  the  constancy  of  this  ratio 
of  the  velocity-changes  enables  us  to  give  a 
number  to  each  body,  which  is  characteristic 
of  its  inertia.  Let  me  remind  you  of  how  we 
give  a  number  to  the  length  of  a  table:  we 
select  arbitrarily  a  certain  rod,  and  call  its 


MASS  15 

length  any  number  we  choose,  thus  we  give 
the  number  three  to  a  yardstick, — and  then 
by  a  method  of  superposition  we  ascertain 
how  many  times  the  length  of  this  rod  is  con- 
tained in  that  of  the  table.  So  here  in  the 
case  of  these  impact  experiments,  let  us  call 
the  change  in  the  velocity  of  one  body  by  the 
symbol  c1}  and  that  in  the  velocity  of  the  other, 

c2,  and,  remembering  that  their  ratio  -  is  al- 

C2 

ways  the  same  for  the  same  two  bodies,  we 
can  give  arbitrarily  a  number,  ml9  to  the  first 
body  and  then  define  the  corresponding  num- 
ber for  the  second  body  to  be  given  by  a 
number,  m2,  such  that 

m2  =  raj  £ 

C2 

This  gives  us,  then,  a  definite  number  for  the 
second  body.  Let  us  see  what  property  of  the 
body  this  number  measures.  It  is  evident  from 
the  definition  that,  if  the  change  in  the  motion 
of  the  second  body  is  small,  the  value  of  m  is 
large,  and  vice  versa;  so  that  the  size  of  m 
corresponds  to  the  opposition  offered  by  the 


16  THE  CONSTITUTION  OF  MATTER 

body  to  having  its  motion  changed ;  this  prop- 
erty is  what  we  think  of  when  we  speak  of 
the  "  quantity  of  matter  "  in  a  body,  and  it 
was  called  by  Newton  its  "  mass." 

In  a  similar  manner,  by  suspending  a  third 
body  in  place  of  the  second,  and  using  the 
same  number  m,l  for  the  first  body,  we  may 
obtain  a  number  m3  for  the  mass  of  this,  etc. 
Newton  convinced  himself  that  this  mode  of 
assigning  numbers  to  the  mass  of  a  body  was 
perfectly  consistent ;  and  we  adopt  it  as  our 
definition  of  "  mass." 

We  can  get  more  familiar  illustrations  of 
this  idea  of  mass  if  we  consider  other  cases  of 
the  interaction  of  two  bodies.  Thus,  if  a  man 
standing  on  a  board  which  rests  on  smooth 
ice  jumps  sidewise,  the  board  will  be  pushed 
in  the  opposite  direction ;  and,  if  the  man  has 
a  greater  mass  than  the  board,  his  velocity 
will  be  less.  When  a  bullet  is  expelled  from  a 
gun,  there  is  a  recoil  of  the  latter ;  and,  owing 
to  the  small  mass  of  the  bullet,  its  velocity  is 
great.  (In  both  these  last  cases  it  should  be 
noted  that,  since  the  motion  begins  from  rest, 


MASS  17 

the  change  in  the  velocity  becomes  the  velocity 
resulting  from  the  interaction  of  the  bodies.) 

It  is  evident,  then,  that  the  mass  of  a  body 
is  a  real  property  of  that  body,  just  as  much 
so  as  its  shape,  size,  or  color.  We  do  not  rec- 
ognize it  by  our  senses  of  sight,  or  touch,  or 
taste;  but  it  is  apparent  to  us  through  our 
muscle-sense  when  we  change  the  motion  of 
the  body.  The  genius  of  Newton  was  never 
shown  more  clearly  than  in  his  conception  of 
this  fundamental  property  of  matter  and  in 
his  introduction  of  it  into  the  expression  or 
description  of  natural  phenomena. 

It  is  obvious,  of  course,  that  the  exact 
number  assigned  to  the  mass  of  any  body  de- 
pends upon  the  choice  of  a  standard  body  of 
reference  and  the  number  given  it ;  but,  if  the 
latter  is  changed,  or  if  different  nations  adopt 
different  standards,  the  only  effect  is  to  change 
in  the  same  ratio  the  numbers  given  the 
masses  of  all  bodies.  The  English-speaking 
people  express  mass  in  terms  of  "pounds"; 
while  the  scientific  unit  is  the  "gram." 

We  have  used  for  purposes  of  definition 


18          THE  CONSTITUTION  OF  MATTER 

an  impact  experiment,  which  is  applicable  only 
to  solid  bodies,  but  other  methods  for  deter- 
mining the  values  of  mass  have  been  devised, 
which  can  be  used  for  all  kinds  of  bodies, 
solids,  liquids,  or  gases. 

When  accurate  methods  of  measurement 
are  used,  a  most  important  fact  is  discovered ; 
namely,  the  mass  of  a  body  is  definitely  char- 
acteristic of  it;  it  cannot  be  changed.  We 
can  easily  alter  its  shape,  size,  color,  etc.,  e.g., 
by  raising  its  temperature  or  by  twisting  it ; 
but  the  mass  remains  unaffected.  If  a  block 
of  ice  melts,  or  if  the  resulting  water  is 
changed  into  steam,  we  believe  that  there  is 
no  change  in  the  mass.  If  a  body  is  broken 
into  fragments;  or  if  two  or  more  bodies 
unite  to  form  one,  the  mass  of  the  whole  is 
found  to  equal  the  sum  of  the  masses  of  the 
parts.  This  general  statement  is  called  the 
principle  of  the  te  conservation  of  matter." 

In  the  course  of  these  lectures  it  will  be 
shown  that  there  are  other  things  in  nature 
than  material  bodies — as  we  use  these  words 
ordinarily  —  which  possess  mass;  and  in  the 


MOMENTUM  19 

complete  statement  of  all  laws  referring  to 
mass,  these  must  be  included.  As  a  matter  of 
fact,  however,  this  additional  mass  does  not 
enter  into  our  ordinary  experience. 

Returning  for  a  moment  to  the  impact  ex- 
periment, we  can  easily  see  that  there  is  an- 
other mode  of  description,  which  is  perhaps 
more  easily  remembered.  The  numbers  as- 
signed the  masses  of  the  two  bodies  were  so 
selected  as  to  be  inversely  proportional  to  the 
changes  in  the  velocity ;  that  is,  using  the 
same  symbols  as  before,  — 

m2_£i 

rax  ~  c2 

or  mjCx  =  W2c2  numerically. 

But  the  changes  in  velocity  are  opposite  in 
direction;  if  one  is  an  increase,  the  other  is  a 
decrease;  so  we  may  state  all  the  facts  by 

writing 

m^  =  -  ra2c2 

The  product  of  mass  by  velocity  is  called 
"momentum";  thus  m^  is  the  change  in 
momentum  of  the  first  body,  and  m2c2  is  that 
of  the  second.  Hence  we  see  that  the  increase 


20  THE  CONSTITUTION  OF  MATTER 

of  momentum  of  one  body  is  equal  to  the  de- 
crease of  momentum  of  the  other;  which  is 
equivalent  to  saying  that  the  total  momentum 
of  the  two  does  not  change  during  the  impact. 

This  idea  of  momentum  is  of  fundamental 
importance  in  our  concept  of  mass.  Our  first 
approach  to  it  comes  through  an  experiment 
consisting  in  stopping  a  moving  body,  and  the 
intensity  of  the  sensation,  depending,  as  it 
does,  upon  both  the  body  and  its  velocity, 
really  measures  its  momentum.  We  must  note 
further,  that  when  we  say  that  a  body  has  a 
definite  velocity,  we  mean  that  it  is  moving 
in  a  definite  direction  with  a  definite  speed ; 
and  therefore,  if  we  have  a  collection  of  bodies 
moving  in  different  directions,  their  effective 
momentum  in  any  one  direction  can  be  found 
from  the  momenta  of  the  separate  bodies  only 
by  making  allowance  for  the  directions  of 
motion.  Thus  a  bullet  striking  a  target  ob- 
liquely does  not  impart  as  great  a  blow  as  if 
it  had  struck  it  perpendicularly. 

The  substance  of  what  I  have  said  thus  far 
about  mass  is  this :  there  is  a  definite  property 


MOMENTUM  21 

of  matter,  called  its  mass,  of  which  we  become 
conscious  through  our  muscle-sense;  but  the 
intensity  of  the  sensation  depends  upon  the 
change  produced  in  the  momentum,  that  is 
the  product  of  mass  and  velocity.1 

The  change  in  motion  of  which  we  have 
spoken  in  these  impact  experiments  of  New- 
ton is,  of  course,  the  total  change  between 
the  two  instants  when  impact  begins  and 
when  it  ends;  the  change  goes  on  during  the 
interval  between  these,  but  it  is  difficult  to 
observe  the  change  for  any  portion  of  it.  In 
other  cases  of  change  of  motion,  however, 
this  is  distributed  over  a  sufficient  interval  of 
time  for  one  to  study  it  more  in  detail.  At 
any  given  instant  the  motion  is  changing  at  a 
definite  rate  per  unit  of  time;  this  is  called 
the  "acceleration."  Newton  formulated  cer- 
tain hypotheses  in  regard  to  changes  of  mo- 
tion in  bodies,  which  he  showed  were  actually 

1  Galileo  perceived  clearly  that  in  all  impact  or  similar 
experiments  the  effects  produced  depended  upon  two  proper- 
ties of  the  body  concerned ;  one,  internal,  the  same  always 
for  the  same  body  ;  the  other  external,  conditioned  by  its 
velocity. 


22          THE  CONSTITUTION  OF  MATTER 

verified  so  far  as  observation  permitted  him  to 
say.  These  may  be  stated  as  follows:  — 

(1)  Whenever  the  motion  of  a  body  changes, 
it  is  owing  to  what  we  may  call  the  "  action  " 
of  another  body;  i.e.,  the  motion  of  a  body 
left  to  itself  would  never  change.  (This  idea 
was  also  held  by  Galileo,  many  years  before 
Newton.) 

(2)  When  two  bodies  which  are  free  to 
move  do  act  on  each  other,  the  motion  of  each 
is  changed  and  in  such  a  manner  that  calling 
«!  and  02  the  accelerations  at  any  instant,  and 
m1  and  m^  the  masses,  a±  and  a^  are  in  oppo- 

site directions,  and  numerically  —  =  —  .  That 

J 


is,  m^  equals  m2a2  numerically,  but  is  oppo- 
site in  direction:  "Action  and  reaction  are 
equal  and  opposite."  (The  particular  point  of 
the  body  whose  acceleration  is  indicated  by  a 
is  what  is  called  the  "center  of  mass."  It  is 
easily  determined  by  experiment  or  by  calcu- 
lation; e.g.,  it  is  the  center  of  a  uniform 
sphere,  the  middle  point  of  a  uniform  rod, 
etc.) 


FORCE  23 

(3)  If  three  or  more  bodies  are  interacting 
simultaneously,  each  simple  action  between 
any  two  bodies  is  the  same  as  if  the  other 
bodies  were  not  present;  and  the  total  accel- 
eration of  any  one  body  is  the  combined  re- 
sult of  the  separate  actions  of  all  the  other 
bodies. 

Therefore,  calling  a  the  acceleration  at  any 
instant  of  a  body  whose  mass  is  m,  the  prod- 
uct ma  is  in  every  sense  a  proper  measure 
of  the  external  agencies  acting  on  it  at  that 
instant.  If  there  is  no  acceleration,  it  does  not 
imply  that  there  are  no  external  agencies,  but 
that,  if  there  are  any,  their  actions  neutralize 
each  other. 

In  describing  changes  of  motion  of  bodies, 
Newton  introduced  a  form  of  words  which  has 
proved  to  be  most  convenient.  Whenever  a 
set  of  conditions  exists  under  which  a  body 
experiences  an  acceleration,  we  say  "  a  force  is 
acting  on  the  body  " ;  and  the  product  of  the 
numerical  values  of  the  mass  of  the  body  and 
of  its  acceleration  is  taken  as  the  numerical 
value  of  the  force.  Thus,  we  speak  of  the 


24          THE  CONSTITUTION   OF  MATTER 

"  force  of  gravity/'  meaning  that,  if  a  body 
is  released  so  as  to  be  free  to  move,  it  will 
have  an  acceleration  towards  the  earth;  we 
speak  of  the  force  due  to  the  tension  in  a 
string,  meaning  that,  if  a  string  attached  to 
a  body  is  suddenly  stretched,  the  body  will  be 
accelerated,  etc. 

If  we  have  any  method  by  which  we  can 
subject  a  body  to  a  force  of  a  known  magni- 
tude, we  can  determine  the  mass  of  the  body 
by  measuring  its  acceleration  under  the  action 
of  the  force,  because  by  definition  the  mass 
equals  the  value  of  the  force  divided  by  that 
of  the  acceleration.  Using  everyday  language, 
we  may  say  that  a  body  offers  an  opposition  to 
having  its  state  of  motion  changed ;  this  op- 
position equals  the  product  of  the  acceleration 
by  the  mass. 

This  concept  of  mass  as  a  fundamental 
property  of  a  body  is  due  to  Newton,  although 
Galileo  recognized  its  existence.  Up  to  within 
very  recent  years  it  has  been  accepted  as  an 
elementary  idea,  i.e.,  it  could  not  be  shown 
that  it  was  due  to  any  other  property  of  a 


WEIGHT  25 

body.  Now,  however,  we  can  prove,  as  will  be 
done  in  a  later  lecture,  that  the  fact  of  a 
body's  having  mass  is  in  all  probability  to  be 
attributed  to  more  fundamental  properties. 

The  second  property  of  matter  to  which 
our  attention  is  called  by  our  muscle-sense  is 
that  to  which  we  ordinarily  give  the  name 
"  weight."  If  one  holds  a  body  in  his  open 
hand,  he  is  conscious  of  this ;  and  if  he  allows 
it  to  fall,  it  will  acquire  an  acceleration,  which, 
as  Galileo  showed,  is  constant  and  the  same 
for  different  bodies.  If  we  call  this  accelera- 
tion g  and  the  mass  of  the  body  m,  we  may 
describe  the  fact  by  saying  that  the  "earth 
exerts  a  force  mg  upon  the  body."  The  idea 
occurred  to  Newton  that  there  ought  to  be  a 
similar  action  in  the  case  of  any  two  bodies, 
e.g.,  the  earth  and  the  moon  or  the  sun ;  and 
he  formulated  a  hypothesis  as  to  the  value  of 
the  force  in  the  general  case,  which,  so  far  as 
all  known  observations  furnish  us  the  truth, 
has  been  completely  verified  for  bodies  of 
moderate  or  large  dimensions.  The  funda- 
mental facts  concerning  this  aspect  of  matter 


26          THE  CONSTITUTION   OF  MATTER 

are,  then,  (1)  that  any  two  bodies,  if  not  too 
small,  will,  if  free  to  move,  approach  each 
other,  and  (2)  that  the  law  of  action  is  known. 
This  property  is  called  gravitational  action, 
and  will  be  described  in  another  lecture ;  but 
it  should  be  noted  here  that  this  gravitational 
force  depends  only  upon  the  masses  of  bodies 
and  their  distances  apart,  not  upon  their  mate- 
rial. 

The  third  property  of  matter  of  which  we 
spoke  is  the  one  to  which  our  attention  is 
called  by  our  muscle-sense  when  we  attempt 
to  change  the  size  or  shape  of  a  portion  of 
matter.  We  recognize,  as  a  matter  of  fact,  a 
great  number  of  properties  all  of  which  may, 
in  a  certain  sense,  be  grouped  together  :  rigid- 
ity, hardness,  plasticity,  etc.  Certain  of  these 
are  typical  of  what  we  call  solids,  others  of 
liquids,  others  of  gases.  The  fundamental  fact 
is  that  the  minute  portions  of  all  bodies  act 
upon  each  other  with  forces  which  vary  in  all 
possible  ways  and  which  give  to  different  bod- 
ies distinctive  properties.  These  will  be  dis- 
cussed later. 


THE   AETHER  27 

To  summarize  what  has  been  said :  every 
portion  of  matter  has  a  definite  property 
measured  by  its  mass ;  two  portions  of  mat- 
ter, if  not  too  small,  attract  each  other  ac- 
cording to  a  simple  law  which  is  independent 
of  the  kind  of  matter ;  two  minute  portions  of 
matter  act  upon  each  other  in  a  manner  vary- 
ing with  the  kind  of  matter.  In  addition  to 
these  properties  which  are  concerned  with 
either  a  single  portion  of  matter  or  with  two 
portions,  there  is  another  most  important  one 
which  requires  considerable  discussion. 

One  of  the  most  useful  concepts  in  the  his- 
tory of  science  is  that  of  the  so-called  "  lumi- 
niferous  ether,"  or  as  English  writers  call  it 
"the  aether."  It  is  pictured  as  a  universal 
medium,  filling  all  known  space ;  in  this  the 
minute  portions  of  ordinary  matter  are  sup- 
posed to  exist,  not  unlike  the  motes  of  dust 
one  sees  in  the  air  of  a  room  when  a  ray  of 
sunlight  enters.  It  is  assumed,  further,  to  have 
mass  and  to  be  capable  of  sustaining  a  strain, 
like  an  elastic  piece  of  matter.  Perhaps  I  should 
use  the  expressions  "  was  "  and  "  has  been," 


28          THE  CONSTITUTION  OF  MATTER 

because,  to  many  people,  the  idea  of  such  a 
medium  is  not  essential  for  a  picture  of  nature ; 
but  it  still  plays,  and  undoubtedly  will  con- 
tinue to  do  so,  a  useful  part  in  our  language 
and  in  our  ideas.  The  primary  function  of  the 
aether  was  that  of  serving  as  a  vehicle  of  the 
cause  of  light.  The  sun  produces  in  our  eyes 
the  sensation  of  light ;  and  observations  prove 
that  whatever  it  is  that  the  sun  emits  and  that, 
when  it  reaches  our  eyes,  produces  light,  it 
travels  through  space  with  a  definite  velocity 
of  30,000,000,000  (or  3  X 1010)  centimeters  per 
second,  or  about  186,000  miles  per  second. 
We  can  picture  this  emission  from  the  sun  as 
consisting  of  discrete  particles  or  as  being  a 
wave-motion.  Particles  in  the  ordinary  sense 
it  cannot  be ;  and,  if  it  is  wave-motion,  a  me- 
dium is  required,  whose  motion  shall  constitute 
the  waves.  The  aether  was  the  name  given  this 
medium.  This  conception  of  the  aether  may 
best  be  understood  with  reference  to  the  con- 
cept of  energy,  to  the  discussion  of  which 
some  time  must  be  devoted. 

We  often  introduce  into  science  from  every- 


ENERGY  29 

day  language  certain  words  to  which  we  give 
exact  definition.  Thus  the  word  "  work  "  has 
been  adopted  and  has  been  defined  as  having 
a  value  equal  to  the  product  of  the  values  of  a 
force  and  of  the  distance  in  its  line  of  action 
through  which  its  point  of  application  moves. 
If  I  raise  a  heavy  body  vertically  upward,  I 
do  work  to  an  amount  equal  to  the  product  of 
the  weight  by  the  height  through  which  I 
raise  the  body.  If  I  throw  a  ball  whose  mass 
is  m  so  as  to  give  it  an  acceleration  a,  a  force 
ma  is  required,  and,  if  I  move  my  hand  a  dis- 
tance x  in  producing  the  final  velocity,  I  do 
the  work  max.  These  illustrate  the  two  ways  in 
which  mechanical  work  may  be  done :  (1)  over- 
coming an  opposing  force,  such  as  gravity; 
(2)  producing  acceleration.  As  the  result  of 
the  work  done  upon  a  body  in  either  of  these 
ways,  the  body  itself  gains  the  power  of  doing 
work.  Thus,  the  elevated  body  can  do  work 
by  falling  again  ;  e.g.,  it  may  fall  upon  a  board 
and  bend  it,  or  it  may  give  motion  to  another 
body  by  striking  it ;  the  moving  ball  can  do 
work ;  e.g.,  if  it  strikes  another  ball,  it  may 


30          THE   CONSTITUTION  OF  MATTER 

set  it  in  motion.  We  must  specially  notice  that 
in  all  cases,  if  the  body  does  work,  as  stated, 
the  power  of  doing  more  work  is  diminished. 
When  a  body  has  this  power  to  do  work,  it  is 
said  to  possess  "energy."  Therefore,  as  it 
does  work,  it  loses  energy;  and  the  loss  in 
energy  in  any  case  is  defined  to  be  equal  to 
the  work  done.  Conversely,  when  the  body 
has  work  done  upon  it,  it  gains  energy.  If  it 
gains  this  energy  as  the  result  of  work  done  in 
overcoming  a  force,  the  energy  is  called  "  po- 
tential," e.g.,  an  elevated  body,  a  coiled  watch- 
spring,  a  bent  bow  have  potential  energy. 
When  the  body  has  gained  energy  as  the  re- 
sult of  work  done  upon  it  in  giving  it  motion, 
the  energy  is  called  "  kinetic  " ;  e.g.,  a  falling 
body,  a  flying  bullet,  a  revolving  fly-wheel,  all 
have  kinetic  energy.  If  a  body  whose  mass  is 
m  is  moving  with  a  velocity  v,  the  value  of  its 
kinetic  energy  may  be  shown  to  be  £  mi?. 

We  may  say,  then,  that  a  system  has  poten- 
tial energy  if  it  is  not  in  its  "  natural "  condi- 
tion ;  thus  a  body  may  be  thought  to  be  in  its 
natural  condition  with  reference  to  the  earth, 


ENERGY  31 

if  it  is  in  contact  with  it ;  and,  when  separated 
from  the  earth,  the  system,  involving  it  and 
the  earth,  has  potential  energy.  An  elevated 
body  falls  if  it  is  allowed  to,  a  coiled  spring' 
uncoils  if  it  is  free  to  do  so,  a  bent  bow  un- 
bends when  released,  etc.;  all  of  these  "  relax- 
ing "  processes  involve  a  decrease  in  potential 
energy.  Consequently,  we  may  say  that,  when 
a  system  at  rest  has  potential  energy,  all  mo- 
tions or  changes  which  can  take  place  of  them- 
selves occur  in  such  a  manner  as  to  cause  a 
decrease  in  potential  energy.  (This  is  a  mode 
of  describing  actions  which  sometimes  is  pref- 
erable to  the  use  of  the  word  "  force.") 

If  we  picture  to  ourselves  any  series  of  me- 
chanical processes  involving  work  (e.g.,  let  a 
compressed  spiral  spring  give  velocity  to  a  ball, 
let  this  ball  strike  another  ball  giving  it  veloc- 
ity, let  this  second  ball  strike  a  steel  spring 
and  bend  it,  etc.),  we  see  that  work  is  done  at 
each  of  the  stages,  one  body  losing  energy, 
the  other  body  gaining  it.  In  accordance  with 
our  definitions,  the  amount  of  energy  which 
the  one  loses  equals  that  gained  by  the  other; 


32          THE  CONSTITUTION  OF  MATTER 

work  is  involved  in  the  "transfer"  of  the 
energy.  The  total  amount  of  energy,  then,  in 
the  system  remains  unchanged.  This  consti- 
tutes the  simplest  illustration  of  the  principle 
of  the  "  conservation  of  energy." 

I  have  purposely  limited  the  discussion  and 
the  range  of  illustration  to  mechanical  systems, 
i.e.,  to  heavy  bodies,  springs,  etc.  There  are, 
however,  many  cases  involving  work,  which  lie 
beyond  such  simple  systems.  Thus  if  I  rub 
one  rough  body  against  another,  if  I  stir  a 
paddle  in  water,  work  is  required;  and  yet 
there  is  no  change  in  position  and  no  appar- 
ent resulting  motion  to  indicate  a  gain  of 
energy  by  the  rough  bodies  or  by  the  water. 
We  do  find,  however,  that  in  both  cases  the 
bodies  on  which  the  work  has  been  done  in- 
dicate a  rise  in  temperature  and  other  so-called 
"heat-effects."  This  leads  to  the  hypothesis 
that  the  work  done  in  rubbing  or  in  stirring 
has  been  spent  in  affecting  the  condition,  not 
of  the  bodies  as  wholes,  but  of  their  minute 
portions ;  that  is,  if  there  are  forces  holding 
together  these  portions,  work  may  have  been 


RADIANT  ENERGY  33 

done  in  overcoming  them ;  and,  if  these  por- 
tions are  free  to  move,  kinetic  energy  may 
have  been  given  them.  This  idea  of  consider- 
ing the  minute  portions  of  a  body  as  having 
both  potential  and  kinetic  energy,  and  of  asso- 
ciating heat-effects  and  heat-phenomena  in 
general  with  the  changes  in  this  internal  energy 
of  bodies,  has  been  completely  justified  by  ex- 
periments. By  giving  proper  numbers  to  the 
various  heat-quantities  involved  in  these,  we 
find  that  we  can  extend  the  principle  of  the 
conservation  of  energy  so  as  to  include  the 
heat-phenomena  as  well  as  the  ordinary  mo- 
tions of  mechanics. 

As  has  just  been  said,  one  of  the  results  of 
doing  work  upon  a  body,  so  as  to  add  energy 
to  its  minute  parts,  is  rise  in  temperature. 
This  same  effect  is  produced  if  we  expose  a 
body  to  the  sun's  rays.  This  means  that  the 
body  is  gaining  energy  from  the  sun  ;  the 
latter  emits  it  and,  after  a  lapse  of  time  de- 
pending upon  the  distance  of  the  sun  from 
the  earth,  the  body  receives  it.  During  the 
time  of  transit  from  the  sun  to  the  earth  this 


34          THE  CONSTITUTION   OF  MATTER 

energy  is  referred  to  as  "  radiant  energy  "  or 
"radiation."  To  all  who  believe  in  the  reality 
of  the  aether  this  radiation  is  energy  due  to 
motions  and  strains  in  this  medium;  and  it 
advances  through  the  aether  by  the  same  gen- 
eral process  as  a  wave  travels  along  a  stretched 
cord  one  of  whose  ends  is  vibrated.  Part  of 
this  energy  is  kinetic ;  and  part  is  to  be  con- 
sidered potential. 

One  of  the  most  interesting  chapters  of  the 
history  of  science  is  that  which  contains  the 
proof  that  every  portion  of  matter  in  the  uni- 
verse is  emitting  radiant  energy  and  also  has 
the  possibility  of  receiving  such  energy  com- 
ing from  other  portions  of  matter.  (It  is  evi- 
dent that,  if  we  can  imagine  this  radiant 
energy  as  an  entity  by  itself,  there  is  no  need 
of  forming  the  conception  of  the  a3ther  to  carry 
it;  and  this  idea  is  now  held  by  many.) 

I  cannot  leave  this  subject  of  energy  with- 
out referring  briefly  to  one  or  two  other  mani- 
festations of  it.  As  we  shall  see  when  electrical 
phenomena  are  discussed  in  a  later  lecture,  it 
requires  work  to  produce  electrification  and 


ENERGY  35 

also  to  produce  an  electric  current ;  this  means 
that  energy  is  associated  with  these  two  phe- 
nomena. In  the  case  of  ordinary  charged 
bodies  this  energy  is  to  be  thought  of  as 
"potential,"  because  motions  take  place  in 
such  a  manner  as  to  decrease  it ;  further,  as 
we  so  far  understand  the  phenomenon  of 
electrification,  we  are  unable  to  show  that  it 
is  associated  with  any  motions.  On  the  other 
hand,  the  phenomena  of  an  electric  current 
are  essentially  kinetic  in  character,  motions 
are  involved  in  every  feature ;  and  therefore 
the  energy  associated  with  a  current  is  treated 
as  "kinetic."  It  will  be  noted  that  neither  in 
the  case  of  electrification  nor  in  that  of  the 
current  have  I  spoken  of  the  energy  as  being 
associated  with  anything.  Those  who  believe 
in  the  aether  think  of  it  as  being  the  seat  of 
both  these  kinds  of  energy ;  while  others  con- 
sider the  energy  as  having  an  independent 
existence. 

We  think  then  of  energy  as  existing  in 
many  forms,  associated  with  matter  and  with 
the  aether,  potential  and  kinetic ;  and  to  the 


36          THE  CONSTITUTION  OF  MATTER 

best  of  our  knowledge  the  total  amount  of 
energy  is  conservative.  Kinetic  energy  seems 
to  us  more  easily  understood,  because  when 
associated  with  ordinary  matter  its  numerical 
value  is  J  mv* ;  potential  energy,  on  the  other 
hand,  is  a  purely  mathematical  expression  and 
cannot  be  analyzed  into  any  mechanical  pic- 
ture ;  radiant  energy,  consisting  as  it  does  of 
wave-motion,  is  a  concept  which  we  can  com- 
pare, for  many  purposes,  with  well-known 
mechanical  disturbances. 

Having  thus  far  discussed  the  more  obvious 
properties  of  material  bodies,  let  us  now  con- 
sider what  is  known  about  their  constitution. 
If  we  break  into  parts  any  piece  of  matter, 
e.g.,  a  drop  of  water  or  a  copper  wire,  each  of 
the  portions  retains  the  properties  of  the  whole. 
If  the  matter  is  homogeneous,  we  can  imagine 
this  process  of  subdivision  continued  almost 
indefinitely.  All  experiments  go  to  prove  that 
ultimately  we  shall  obtain  a  portion  of  matter 
so  minute  that,  although  still  being  like  the 
parent  substance,  it  will,  if  broken  up,  give 
rise  to  portions  of  matter  unlike  this  sub- 


MOLECULES  37 

stance.  This  last  minute  fragment  which  still 
retains  the  properties  of  the  original  matter 
is  called  a  "molecule."  The  fragments  into 
which  a  molecule  may  be  resolved  are  as  a  rule 
different ;  but,  if  they  are  all  alike,  the  mole- 
cule is  called  "  elementary/'  and  the  matter  of 
which  it  formed  a  part  is  called  an  "  element." 
The  number  of  known  elements  is  about  100, 
such  as  hydrogen,  oxygen,  mercury,  lead,  iron, 
etc.  When  in  the  course  of  ordinary  chemical 
processes  an  elementary  molecule  is  disrupted, 
the  final  fragments  are  called  "  atoms  "  ;  and 
the  science  of  chemistry  is  based  upon  the 
completely  verified  hypotheses  that  the  atoms 
of  any  element  are  all  alike  and  that  all  mole- 
cules are  composed  of  these  atoms  present  in 
definite  proportions.  Thus,  a  molecule  of 
water  consists  of  two  atoms  of  hydrogen  and 
one  of  oxygen ;  a  molecule  of  sulphuric  acid 
consists  of  two  atoms  of  hydrogen,  one  of 
sulphur,  and  four  of  oxygen. 

We  picture,  therefore,  every  portion  of 
matter  as  made  up  of  molecules,  which  are  in 
some  cases  bound  together  to  form  a  solid, 


38          THE  CONSTITUTION  OF  MATTER 

in  others  not,  as  in  a  gas.  But  in  all  cases  we 
know  that  the  molecules  are  in  unceasing 
motion.  The  evidence  of  this  motion  is  most 
ample :  evaporation  of  a  liquid  consists  sim- 
ply in  the  escape  from  the  surface  of  its  rapidly 
moving  molecules ;  if  any  two  portions  of 
matter  are  brought  into  contact  over  a  surface, 
a  gradual  intermingling  of  molecules  through 
this  surface  may  be  observed,  etc.  In  the  case 
of  a  solid  the  molecules  are  held  more  or  less 
rigidly  in  a  fixed  configuration,  and  simply 
oscillate  to  and  fro ;  in  a  liquid  the  molecules 
wander  with  comparative  freedom  throughout 
the  whole ;  in  a  gas  there  is  still  greater  free- 
dom of  motion. 

If  we  imagine  a  large  space  containing  a 
great  number  of  minute  elastic  spheres  thrown 
in  perfectly  at  random,  they  will  collide,  re- 
bound, hit  against  the  walls,  etc.  The  velocity 
of  any  one  sphere  will  change  in  direction 
and  amount ;  but,  if  we  can  assume  that  there 
is  a  very  large  number  of  spheres  present,  we 
can  calculate  the  pressure  on  the  walls  owing 
to  the  impact  of  the  spheres,  the  proportion 


MOLECULES  39 

of  molecules  which  will  probably  have  any 
specified  velocity  (under  given  conditions),  etc. 
The  properties  of  this  set  of  spheres  correspond 
in  a  wonderful  manner  with  the  observed  prop- 
erties of  a  gas.  So  perfect  is  the  agreement 
that  we  feel  justified  in  applying  to  actual 
gases  certain  formulae  deduced  for  the  be- 
havior of  the  set  of  spheres,  and  which  thus 
enable  us  —  assuming  the  justification  of  the 
method  —  to  form  a  fairly  clear  idea  as  to  the 
number  of  molecules  present  in  any  definite 
volume  of  the  gas,  the  apparent  volume  of  a 
molecule,  the  average  speed  of  a  molecule  at 
any  definite  temperature,  etc.1 

The  fact  that  the  atoms  constituting  the 
molecules  are  also  in  vibratory  motion  cannot 

1  See  Article  "Molecules,"  Encyc.  Brit.t  eleventh  edition. 
A  few  of  these  figures  are  as  follows  :  — 

Diameter  of  a  hydrogen  molecule  is  2XlO~8cm. 

Mean  velocity  at  0°  C.  of  hydrogen  molecules  is  169,400 
cm.  per  sec. 

Numher  of  molecules  per  cubic  centimeter  is  4X1019. 
(This  number  is  too  large,  as  we  shall  see.) 

The  beautiful  experiments  of  Pen-in  have  shown  us  that 
these  laws  deduced  from  the  kinetic  theory  of  matter  are 
verified  in  a  wonderful  manner  by  the  motions  of  the  minute 
groups  of  molecules,  which  are  shown  in  what  is  called  the 
"  Brownian  Movement." 


40          THE  CONSTITUTION  OF  MATTER 

be  doubted.  If  two  bodies,  each  consisting  of 
simpler  parts,  undergo  any  kind  of  collision, 
the  parts  themselves  must  be  affected.  Fur- 
ther, the  dimensions  of  the  disturbances  which 
accompany  the  radiant  energy  emitted  by  all 
bodies  prove  that  the  parts  of  the  molecules 
are  themselves  in  motion. 

One  of  the  most  important  of  the  conclu- 
sions to  be  drawn  from  the  kinetic  theory  is 
a  method  leading  to  the  determination,  not  of 
the  mass  of  molecules,  but  of  the  ratio  of  the 
masses  of  the  molecules  of  any  two  gases.  In 
the  hands  of  chemists  this  has  led  to  the 
perfection  of  methods  for  measuring  the  ratio 
of  the  masses  of  the  known  atoms.  Knowing 
these  ratios,  we  may  assign  any  number  we 
wish  to  the  atom  of  some  one  element,  and 
then  we  have  corresponding  numbers  for  the 
atoms  of  all  the  other  elements.  These  num- 
bers are  called  "  atomic  weights  " ;  and  the 
system  in  most  general  use  is  based  upon  the 
selection  of  the  number  one  for  the  hydrogen 
atom. 

It  has  been  proved,  as  the  result  of  the  work 


PERIODIC  SYSTEM  41 

of  NewlandsjMendeleeflVand  others,  that  if  the 
elements  are  grouped  in  a  rectangular  array, 
seven  elements  in  a  row,  the  arrangement 
being  strictly  in  accordance  with  the  atomic 
weights,  the  elements  falling  in  any  one  column 
have  many  similar  properties.  This  is  known 
as  the  "  periodic  system."  Of  course,  when  the 
first  grouping  was  made,  it  was  necessary  to 
use  judgment  in  deciding  where  any  element 
was  to  be  placed,  because  it  was  always  possi- 
ble that  there  were  still  elements  to  be  discov- 
ered ;  and  therefore  spaces  had  to  be  left  for 
them.  As  time  has  gone  on,  and  new  elements 
have  been  found,  they  have  fallen  into  place 
in  the  table,  so  that  now  nearly  all  the  gaps 
have  been  filled.  Of  course,  modifications  have 
been  made,  such  as  the  extension  of  each  row 
so  as  to  contain  eight  elements,  and  the  collec- 
tion of  certain  elements  into  distinct  sub-groups, 
apart  from  the  main  table.  Since  the  first  dis- 
covery of  this  periodicity,  many  new  features 
have  been  investigated  proving  that  the  ele- 
ments in  any  one  column  must  be  considered 

1  See  article  "  Element,"  Encyc.  Brit.,  eleventh  edition. 


42          THE  CONSTITUTION  OF  MATTER 

as  most  intimately  connected,  in  other  words, 
their  atoms  must  be  believed  to  be  related. 
For  many  years  the  evidence  was  entirely 
chemical;  but  within  the  past  few  years  many 
additional  facts  have  been  discovered  by  means 
of  physical  investigations.  Thus,  the  science 
of  spectroscopy  is  based  upon  the  fact  that 
the  molecules  of  each  element,  when  in  a  gas- 
eous condition,  can  be  so  excited  as  to  emit 
radiant  energy  of  a  quality  which  is  character- 
istic of  that  element;  and  when  the  spectra  of 
the  elements  in  any  column  of  the  table  are 
compared,  it  is  found  that  there  are  definite 
points  of  agreement.  Similarly,  when  Roentgen 
rays  traverse  layers  of  different  materials,  it  is 
found  that  varying  proportions  of  the  energy 
are  absorbed  by  the  matter,  and  that  a  secondary 
radiation  is  produced.  This  is  found  to  be  char- 
acteristic of  the  atoms  making  up  the  mole- 
cules of  the  matter ;  and,  when  the  properties 
of  the  different  elements  are  compared,  it  is 
found  that  they  again  arrange  themselves  in  the 
periodic  system.  The  obvious  interpretation  of 
the  periodicity  observed  is  that  the  atoms  of 


PERIODIC  SYSTEM  43 

the  elements  in  any  one  column  are  related  in 
some  such  way  as  the  following :  one  atom  cor- 
responds to  a  chain  having  ten  links;  the  next 
atom,  to  a  chain  with  eleven  links,  etc.;  or 
starting  with  any  atom,  the  one  below  it  in  the 
column  is  formed  by  the  addition  of  a  shell 
of  matter,  etc.  The  connection  between  the 
elements  in  any  one  row  of  the  table  is  much 
less  obvious,  and  is  more  numerical  than  chem- 
ical or  physical.1 

From  the  early  days  of  chemistry  fruitless 
attempts  have  been  made,  notably  by  Prout,  to 
prove  that  all  the  elements  are  derived  from 
combinations  of  different  numbers  of  a  single 
primordial  atom.  The  first  investigator  to  prove 
that  a  large  number  of  different  elements  con- 
tained a  common  constituent  was  Sir  J.  J. 
Thomson,  of  the  University  of  Cambridge.  It 
has  been  known  for  many  years  that,  when  a 
gas  is  inclosed  in  a  bulb  and  nearly  exhausted, 

1  Rydberg  has  called  attention  to  some  most  important 
connections  between  the  atomic  weights  of  the  elements,  all 
of  which  have  a  bearing  on  this  question.  Zeit.fur  Anorg. 
Chem.,  vol.  xiv,  p.  66  (1897).  See  also  Comstock,  Phil.  Mag., 
vol.  xv,  p.  1  (1908). 


44  THE  CONSTITUTION  OF  MATTER 

so  that  the  pressure  is  extremely  small,  the 
passage1  of  an  electric  current  through  the  gas 
is  accompanied  by  the  production  of  a  stream 
of  rapidly  moving  particles  called  the  u  cath- 
ode rays."  The  current  enters  and  leaves  the 
bulb  by  metal  connections ;  wires  are  inserted 
through  the  walls  and  end  inside  the  bulb 
in  metal  plates.  The  one  by  which  the  cur- 
rent leaves  is  called  the  "  cathode  "  ;  and  the 
"  cathode  rays  "  have  lines  of  motion  perpen- 
dicular to  its  surface.  In  the  investigation  of 
the  nature  of  these  rays,  Thomson  proved  that 
they  were  minute  particles  identically  alike, 
quite  regardless  of  the  nature  of  the  gas  orig- 
inally put  in  the  bulb;  and  to  them  he  gave 
the  name  "  corpuscle."  By  means  of  a  series 
of  brilliant  investigations  he  was  able  to  meas- 
ure the  mass  of  a  corpuscle,  and  he  proved  that 
it  was  approximately  one  eighteen  hundredth 
of  that  of  a  hydrogen  atom.  I  shall  speak  in 
a  later  lecture  of  what  is  meant  by  "  electrical 
charges";  but  you  are  all  familiar  doubtless 

1  See  J.  J.  Thomson,  Conduction  of  Electricity  through  Gases 
(1903). 


CORPUSCLES  45 

with  the  fact  that  we  distinguish  between  two 
conditions  of  electrification  which  we  call  posi- 
tive and  negative;  and  that  we  are  able  to 
measure  charges.  It  has  been  known  for  many 
years  that  the  particles  composing  the  cathode 
rays  in  a  vacuum  tube  were  negatively  charged, 
and  Thomson  devised  a  method  which  proved 
that  the  charges  carried  by  all  corpuscles  were 
the  same  and  which  permitted  the  charge  car- 
ried by  any  one  particle  to  be  measured.  (It  is 
the  same  as  is  carried  by  an  atom  of  hydrogen 
in  the  process  of  electrolysis.)  A  corpuscle, 
then,  is  a  negatively  electrified  particle  of  ex- 
traordinary small  mass;  and  is,  as  Thomson 
showed,  a  common  constituent  of  many  ele- 
mentary gases.  Later  experiments  have  shown 
that  these  same  corpuscles  are  present  in  many 
other  bodies.  Whenever  the  temperature  of  any 
metal  is  raised  sufficiently,  there  is  a  copious 
emission  of  corpuscles,  and  there  is  every  reason 
for  believing  that  there  is  this  same  emission 
at  lower  temperatures,  but  that  our  experi- 
mental methods  are  not  as  yet  sufficiently 
delicate  to  detect  them.  Again,  many  bodies 


46  THE  CONSTITUTION  OF  MATTER 

emit  corpuscles  in  large  numbers  when  light 
falls  upon  them;  and  there  is  a  group  of 
bodies,  known  as  radio-active  substances,  such 
as  radium,  uranium,  thorium,  etc.,  which  emit 
corpuscles  spontaneously.  Still  further  evidence 
that  corpuscles  exist  in  all  elements  is  fur- 
nished by  what  is  called  the  "Zeeman  effect." 
I  have  referred  before  to  the  characteristic 
radiation  emitted  from  all  elements  when  in 
a  luminous  gaseous  condition.  When  such 
an  emitting  gas  is  placed  in  an  intense  mag- 
netic field,  e.g.,  between  the  poles  of  a  strong 
magnet,  there  is  a  slight  change  in  the  character 
of  the  radiation.  In  order  to  account  for  this 
change  it  is  necessary  to  assume  the  existence 
of  small  charged  particles  in  connection  with 
the  atoms ;  and,  when  we  compare  the  observed 
effect  of  the  magnetic  field  with  that  calculated 
from  theory,  it  is  found  that  the  existence  of 
the  corpuscle  is  demonstrated.  Again,  a  dry 
gas  in  its  natural  condition  is  a  very  poor  elec- 
trical conductor;  but  by  certain  processes  it 
may  be  made  an  excellent  one.  When  in  this 
state,  the  gas  is  said  to  be  "ionized";  and  it 


CORPUSCLES  47 

has  been  proved  that  this  condition  is  due  to 
the  presence  in  the  gas  of  corpuscles  ex- 
pelled from  its  molecules  by  the  ionizing 
agent. 

Taking  into  account,  then,  all  evidence,  we 
are  safe  in  believing  that  corpuscles  are  an  es- 
sential part  of  all  atoms.  What  then  forms 
the  rest  of  the  atoms?  Here  again  some  later 
experiments  of  Thomson  offer  knowledge.  It 
was  shown  by  Goldstein  many  years  ago  that, 
if  the  cathode  in  a  "vacuum  tube"  is  perfo- 
rated, there  is  a  special  type  of  radiation  which 
passes  through  these  openings  into  the  space 
back  of  the  cathode  when  an  electric  current 
is  passing  through  the  gas.  To  this  radiation 
he  gave  the  name  "  canal  rays." 1  When  they 
were  investigated  carefully  by  Thomson,  they 
were  found  to  be  positively  charged  particles, 
and  although  when  using  different  gases  in 
the  bulb  particles  of  different  masses  were  ob- 
served, yet  in  all  cases,  no  matter  what  the 
gas  was,  there  were  always  present  particles 

1  See  J.  J.  Thomson,  loc.  cit.;  also,  PUl  Mag.,  vol.  xx, 
p.  752  (1910) ;  vol.  xxi,  p.  225  (1911) ;  vol.  xxv,  p.  209  (1912) ; 
Proc.  Roy.  Inst.  (1911). 


48  THE  CONSTITUTION  OF  MATTER 

having  the  mass  of  a  hydrogen  atom ;  and  in 
no  case  were  there  particles  having  a  smaller 
mass.  The  electric  charge  carried  by  the  hy- 
drogen atom  in  these  canal  rays  is  identically 
the  same  as  that  characteristic  of  the  corpus- 
cle, only  different  in  sign,  being  positive.  The 
other  particles  present  in  these  rays  were  found 
to  be  atoms  of  the  molecules  of  the  gases 
present  in  the  bulb,  or  groups  of  these  atoms. 
As  a  matter  of  fact,  when  we  examine  all 
the  ways  in  which  electrical  charges  appear  in 
nature,  we  find  that  there  is  every  reason  to 
believe  that  all  charges  are  either  equal  to 
that  of  a  corpuscle  or  are  multiples  of  it,  i.e., 
twice  it,  three  times  it,  etc.  In  other  words, 
we  may  call  this  charge  a  true  atom  of  elec- 
tricity, as  was  proposed,  in  another  connection, 
by  Helmholtz.  Further,  the  atomic  negative 
charge  is  always  associated  with  the  corpuscle ; 
and  the  atomic  plus  charge  has  not  yet  been 
found  associated  with  a  particle  less  in  mass 
than  the  hydrogen  atom;  but  we  must  be 
careful  to  remember  that  we  have  not  proved 
that  all  positively  charged  particles  are  com- 


SUMMARY  49 

posed  of  parts  identical  with  the  hydrogen 
atom. 

Another  process  by  which  we  get  evidence 
in  regard  to  these  elementary  particles  is  that 
of  radio-activity.  The  elements  which  possess 
this  property  such  as  uranium,  radium,  etc., 
besides  emitting  corpuscles  as  has  been  al- 
ready stated,  also  expel  positively  charged  par- 
ticles. Rutherford  and  his  associates  have 
proved  that  these  have  the  mass  of  a  helium 
atom  and  carry  twice  the  atomic  charge. 

We  thus  have  conclusive  evidence  that  all 

t 

atoms  of  matter  contain  corpuscles  and  ele- 
mentary positively  charged  particles;  and, 
since  all  matter  in  its  so-called  "  natural "  con- 
dition is  electrically  neutral,  each  atom  must 
in  this  condition  contain  equal  quantities  of 
positive  and  negative  charges ;  so  we  can  form 
a  fairly  clear  idea  of  certain  features  of  any 
atom. 

We  think  of  the  positive  charge  as  occupy- 
ing the  central  part  of  the  atom  of  any  ele- 
ment, and  inside  it,  or  associated  closely  with 
it,  we  picture  a  corresponding  number  of  the 


50  THE  CONSTITUTION  OF  MATTER 

minute  corpuscles.  To  extend  this  idea  so  as 
to  include  atoms  of  different  elements  is  not 
difficult. 

A  question  which  immediately  suggests  it- 
self is  this:  Knowing  that  an  atom  contains 
these  electrical  charges,  can  it  be  shown  that 
what  we  call  mass,  weight,  elasticity  and  radi- 
ation are  consequences  of  the  existence  of 
these  charges?  And,  granting  this,  can  we 
explain  the  periodicity  of  the  elementary  atoms, 
and  the  grouping  of  atoms  to  form  molecules? 

The  fact  that  to  a  great  extent  we  can  do 
this  is  the  most  notable  achievement  of  mod- 
ern science;  and  the  explanation  of  the  vari- 
ous steps  in  the  proof  will  form  the  subject  of 
the  succeeding  lectures. 


II 

CORPUSCLES  AND  ATOMS;    ELECTRICAL 
MASS 

IN  the  preceding  lecture  I  described  a  few  of 
the  more  important  properties  of  matter; 
namely,  mass,  weight,  elasticity,  and  radiation, 
and  described  certain  experiments  which 
proved  that  all  atoms  contained  elementary 
electrical  charges.  Before  we  can  show  the 
connection  between  these  ideas,  it  will  be  nec- 
essary to  discuss  the  properties  of  an  electric 
charge.  We  shall  find  that  there  are  many 
properties  which  we  can  express  in  mathemat- 
ical form,  and  that  a  knowledge  of  this  enables 
us  to  predict  with  confidence  what  will  happen 
under  definite  conditions.  In  this  sense  we 
can  truly  say  that  a  great  deal  is  known  about 
electric  charges;  but  when  any  student  of 
physics  is  asked,  as  he  is  very  often,  "What  is 
electricity?"  he  has  great  difficulty  in  giving 
an  answer.  This  comes  from  the  fact  that  the 


52  THE  CONSTITUTION  OF  MATTER 

one  who  asks  the  question  is  not  satisfied  by 
a  statement  of  the  mathematical  laws  which 
express  our  knowledge  of  electrical  charges 
nor  by  the  statement  that  we  possess  this 
knowledge;  on  the  contrary,  what  the  ques- 
tioner really  means  is,  "  What  does  electricity 
look  like  ?  How  does  it  feel  ?  "  etc.  In  other 
words  the  demand  is  made  implicitly  to  de- 
scribe electricity  in  terms  of  our  senses.  This 
is  impossible.  At  the  present  state  of  our 
knowledge  we  must  consider  an  electric 
charge  as  an  elementary  concept,  and  must 
attempt  to  explain  our  sense-reactions  in 
terms  of  it,  rather  than  to  adopt  the  converse 
process. 

The  study  of  electric  phenomena  has  been 
a  favorite  pursuit  of  philosophers  from  the 
dawn  of  science  ;  and,  owing  to  the  efforts  of 
brilliant  experimenters  and  skillful  mathema- 
ticians, we  can  now  say  that  our  knowledge  of 
the  subject  is  both  extensive  and  accurate.1  I 
must  devote  some  time  to  a  few  of  the  elemen- 

1  See  E.  T.  Whittaker,  A  History  of  the  Theories  ofJElher 
and  Electricity  from  the  Age  of  Descartes  to  the  Close  of  the 
Nineteenth  Century.  Dublin  University  Press  Series  (1910). 


ELECTRIFICATION  53 

tary  facts  before  speaking  of  their  immediate 
bearing  upon  the  subject  in  hand. 

Whenever  we  separate  two  bodies  which 
have  been  in  close  contact,  we  find  that  a  new 
set  of  phenomena  arise  in  connection  with 
them,  namely  small  bits  of  matter,  such  as 
pieces  of  paper,  or  particles  of  dust,  placed 
near  either  of  the  two  bodies  are  attracted 
towards  it.  Strictly  speaking,  the  two  bodies 
in  contact  must  be  of  different  materials ;  but 
as  a  matter  of  fact  no  two  bodies  —  even  if  of 
the  same  material  —  are  identically  alike ;  there 
are  slight  differences  in  the  arrangement  of 
the  molecules.  We  speak  of  these  two  bodies 
as  being  "charged,"  or  "electrified."  In  the 
case  of  some  bodies  it  is  found  that  this  power 
of  attraction  is  localized  in  the  surface  which 
was  in  contact  with  the  second  body ;  whereas 
with  other  bodies  the  power  to  exhibit  attrac- 
tion is  shown  by  its  entire  surface.  The  latter 
class  of  substances  are  called  "  conductors  " ; 
the  former,  "  non-conductors."  Thus,  all  met- 
als are  conductors ;  while  glass,  silk,  flannel, 
rubber  are  non-conductors.  If  any  charged 


64  THE  CONSTITUTION  OF  MATTER 

body  is  suspended  by  cords  so  as  to  be  free 
to  move,  and  if  other  charged  bodies  are 
brought  near,  it  is  observed  that  certain  of  these 
attract  the  suspended  body,  while  all  the  others 
repel  it.  Thus  we  can  divide  all  charged  bodies 
into  two  groups :  call  those  which  attract  by 
the  name  "  A  "  and  those  which  repel  "  B." 
By  now  suspending  any  one  of  the  "  A  "  group 
of  charged  bodies,  we  can  prove  that  it  is  re- 
pelled by  any  other  charge  of  the  same  group, 
but  is  attracted  by  any  one  of  the  "  B  "  group. 
Similarly,  if  one  of  the  "B"  group  is  sus- 
pended, it  is  repelled  by  any  charge  of  the 
same  group,  but  attracted  by  any  one  of 
the  other  group.  Thus  we  may  say  "  like 
charges  repel  each  other ;  unlike  charges  at- 
tract "  ;  meaning  by  "  like  "  charges  those  be- 
longing to  the  same  group.  Various  names 
have  been  given  these  two  groups  of  charges ; 
but  those  in  universal  use  to-day  are  "  positive  " 
and  " negative."  The  name  "positive"  is 
given  to  the  charge  observed  on  ordinary  glass 
rods  when  they  have  been  in  contact  with  silk ; 
and  therefore  all  other  charged  bodies  which 


ELECTRIFICATION  65 

repel  such  a  charged  glass  rod  are  also  posi- 
tively charged ;  while  such  charges  as  attract 
it  are  called  "  negative." 

It  is  worth  noting  that  it  is  a  matter  of  com- 
plete indifference  which  type  of  charge  is  called 
positive  and  which  negative.  The  names  do 
not  imply  excess  or  deficit,  but  simply  oppo- 
site actions  or  motions,  because  in  many 
branches  of  mathematics  a  line  drawn  in  one 
direction  is  called  positive,  and  one  drawn  in 
the  opposite,  negative.  Thus  a  line  vertically 
upward  might  be  called  positive,  in  which  case 
one  drawn  downward  would  be  called  negative. 
A  mechanical  analogy  is  as  follows :  if  holding 
the  ends  of  a  rubber  cord  in  our  two  hands 
we  stretch  it,  the  forces  acting  at  the  two  ends 
are  in  opposite  directions;  if  we  called  one 
positive,  we  would  naturally  call  the  other 
negative. 

We  must  remember,  further,  that  the  ques- 
tion as  to  the  character  of  charge  which  any 
body  assumes,  e.g.,  a  glass  rod,  depends,  not 
alone  upon  the  body  itself,  but  also  upon  the 
body  which  must  be  brought  into  contact  with 


56  THE  CONSTITUTION  OF  MATTER 

it  in  order  to  produce  the  state  of  electrifica- 
tion. Thus  a  glass  rod  will  be  found  to  be 
negatively  charged  after  it  has  been  in  con- 
tact with  fur,  such  as  a  cat's  skin.  This  shows 
that  the  state  and  quality  of  electrification 
depends  upon  the  relative  actions  of  the  two 
kinds  of  molecules  making  up  the  bodies  in 
contact. 

We  have  described  how  we  produce  the 
condition  known  as  electrification,  and  what 
is  meant  by  positive  and  negative  charges. 
Further  experiments  show  that  the  production 
of  a  positive  charge  is  always  accompanied  by 
that  of  a  negative  one ;  that  is,  for  instance, 
when  glass  and  silk  are  brought  in  contact 
and  then  separated,  the  glass  is  positively 
charged,  the  silk,  negatively. 

Through  the  brilliant  experiments  of  Cav- 
endish and  of  Faraday  it  was  proved  that  it 
was  proper  to  speak  of  the  "quantity  of  a 
charge"  and  possible  to  give  a  number  to  it, 
in  terms  of  any  suitable  unit.  Since,  when  two 
bodies  are  in  contact,  there  is  no  evidence  of 
electrification,  and  when  they  are  separated, 


ELECTRIFICATION  57 

there  is  positive  charge  on  one  and  negative 
on  the  other,  the  quantities  of  positive  and 
negative  charges  must  be  equal;  for  then, 
when  they  were  close  together,  there  would 
have  been  no  external  action.  Similarly,  if  at 
every  point  of  a  body  there  are  equal  amounts 
of  positive  and  negative  charges,  there  is  no 
external  evidence  of  a  charge,  and  we  would 
therefore  call  the  body  "neutral"  with  refer- 
ence to  electrification. 

The  discussion  of  the  units  in  terms  of  which 
charges  are  expressed  is  too  complicated  to  be 
given  here.  In  practice  there  are  two;  one  is 
called  the  "  electrostatic  unit " ;  the  other,  the 
"electromagnetic  unit."  One  of  the  latter 
units  equals  3  X  1010  of  the  former. 

Since  there  is  attraction  between  unlike 
charges,  work  is  required  on  our  part  in  order 
to  separate  the  two  bodies  which  have  been  in 
contact,  and  consequently  there  is  energy  as- 
sociated with  charges.  This  energy  is  spoken 
of  as"  electrostatic,"  for  obvious  reasons,  and 
must  be  included  under  the  general  head  of 
potential  energy. 


58  THE  CONSTITUTION  OF  MATTER 

The  exact  mathematical  expression  of  the 
phenomena  observed  in  connection  with 
charged  bodies  was  given  almost  as  soon  as 
the  phenomena  themselves  were  discovered; 
and  we  now  have  at  our  disposal  a  most  com- 
plete mathematical  analysis. 

Quite  a  different  set  of  phenomena  arise 
when  the  charges,  instead  of  being  at  rest, 
are  in  motion.  This  state  can  be  brought  about 
in  two  ways  :  the  charged  body  itself  can  be 
moved ;  or,  the  conductor  being  at  rest,  a  dif- 
ference in  electrical  conditions  may  be  set  up 
at  two  of  its  points.  These  conditions  will  be 
described  more  fully  in  a  later  lecture;  but  it 
is  sufficient  to  say  here  that  the  result  is  to 
secure  a  motion  of  charges  in  the  conductor. 
This  constitutes  an  "  electric  current "  ;  the 
"  direction  "  of  which  is  by  definition  that  in 
which  the  positive  charge  is  moving,  or  oppo- 
site to  that  in  which  the  negative  charge  is 
moving.  An  electric  current  cannot,  of  course, 
be  seen  ;  but  it  is  manifest  to  us  by  the  fact 
that  it  is  accompanied  by  what  is  called  a 
"  magnetic  field " ;  i.e.,  a  condition  under 


ELECTRIC   CURRENT  59 

which  a  magnet  — such  as  a  compass  needle  — 
is  acted  upon  by  a  force.  Naturally  work  is 
required  to  produce  this  motion  of  the  charges, 
and  therefore  a  current  is  always  associated 
with  energy,  which  is  called  "  electrokinetic." 
Here  again  the  mathematical  expression  of  the 
phenomena  is  most  satisfactory. 

I  have  spoken  without  any  hesitation  of 
positive  and  negative  charges,  and  have  shown 
how  the  names  arose  to  describe  certain  con- 
ditions of  experiment.  I  have  also  given  in  the 
last  lecture  the  evidence  in  favor  of  believing 
in  the  existence  of  an  entity  which  we  have 
called  the  corpuscle  and  which  is  the  atomic 
negative  charge,  and  have  said  that  an  atom 
of  matter  in  its  "  natural  "  condition  does  not 
show  any  evidence  of  a  charge.  In  terms  of 
positive  and  negative  electricity,  this  is  ex- 
pressed by  saying  that  in  this  condition  an 
atom  contains  equal  amounts  of  positive  and 
negative  charges.  But  we  may  look  upon  the 
question  from  a  different  standpoint.  We  may 
consider  the  atom  of  matter  as  an  entity,  and 
may  say  that  its  properties  when  it  has  lost  a 


60  THE  CONSTITUTION  OF  MATTER 

corpuscle  are  those  which  we  ordinarily  attrib- 
ute to  a  positive  charge.  In  any  case,  which- 
ever is  our  point  of  view,  there  are  two  dis- 
tinct entities  :  either  the  two  types  of  charges 
which  combine  to  form  an  atom,  or  the  atom 
and  the  corpuscle. 

In  this  connection  we  should  specially  note 
that,  although  we  have  no  proof  of  the  exist- 
ence of  a  positive  charge  carried  on  a  body  of 
less  mass  than  a  hydrogen  atom,  and  although 
in  this  case  the  charge  is  the  atomic  one,  this 
does  not  prove  that  the  atomic  positive  charge 
has  always  the  mass  of  a  hydrogen  atom.  For, 
suppose  that  the  neutral  hydrogen  atom  con- 
tains three  corpuscles  and  therefore  three  unit 
positive  charges.  When  it  loses  one  corpuscle, 
it  will  have  left  two  corpuscles  and  three  unit 
positive  charges,  and  will  consequently  appear, 
in  all  experiments  to  be  charged  with  one 
positive  unit,  although  in  reality  it  contains 
three  atomic  positive  charges.  Therefore  we 
cannot  know  the  actual  mass  associated  with 
a  unit  positive  charge  until  we  know  definitely 
how  many  corpuscles  there  are  in  some  one 


ELECTRIC  WAVES  61 

neutral  atom.  Since  this  number  is  probably 
small,  —  not  far  from  three  for  a  hydrogen 
atom,  as  is  now  believed,  —  the  mass  associated 
with  the  unit  positive  charge  must  be  large 
compared  with  that  of  the  corpuscle,  which 
is  about  one  eighteen  hundredth  of  the  mass 
of  a  hydrogen  atom.  For  this  reason  many  peo- 
ple picture  the  volume  occupied  by  the  posi- 
tive charge  as  being  practically  what  we  may 
call  the  volume  of  the  atom. 

One  of  the  most  important  consequences  of 
the  mathematical  development  of  the  subject 
of  electricity  was  the  proof  by  Maxwell  that 
any  variation  in  the  electrical  conditions  at 
any  point  is  not  accompanied  instantly  by  cor- 
responding changes  in  the  electric  force  at  all 
neighboring  points,  but,  on  the  contrary,  that 
it  takes  a  finite  time  for  the  production  of  the 
changes,  and  that  the  more  remote  the  point 
the  greater  is  the  time  required.  In  other 
words,  disturbances  of  electric  forces  are  prop- 
agated with  a  finite  velocity.  Maxwell's  theory 
went  further,  inasmuch  as  it  gave  the  numeri- 
cal value  for  this  velocity.  In  the  case  of  space 


62  THE  CONSTITUTION  OF  MATTER 

free  of  matter,  e.g.,  between  the  sun  and  the 
earth,  this  velocity  should  be  30,000,000,000 
(or  3  X  1010)  centimeters  per  second.  This  is 
the  observed  velocity  of  light ;  so  we  are  jus- 
tified in  believing  the  phenomena  of  light, 
i.e.,  of  radiant  energy,  to  be  due  primarily  to 
alterations  of  electric  conditions,  to  electric 
oscillations,  as  they  are  called.  In  connection 
with  the  particular  question  which  is  in  our 
minds,  the  explanation  of  the  properties  of 
matter,  we  see  at  once  that  the  fact,  previously 
emphasized,  .of  all  material  bodies  emitting 
radiant  energy  can  be  connected  with  the 
presence  in  the  material  atoms  of  the  electrical 
charges,  provided  these  charges  are  in  such  a 
state  of  motion  as  to  give  rise  to  electric  dis- 
turbances. What  this  state  is  will  appear  pres- 
ently. 

I  must  now  call  your  attention  to  what,  for 
our  present  purposes,  is  the  most  important 
property  of  a  charge.  When  a  charge  is  at 
rest  it  has  associated  with  it,  as  has  been  said, 
a  quantity  of  potential  energy ;  and,  when  in 
motion  of  translation,  it  has  in  addition  a 


ELECTRIC   MASS  63 

definite  amount  of  kinetic  energy,  correspond- 
ing to  the  work  required  to  set  it  in  motion. 
A  moving  charge  is  equivalent  to  a  current; 
and  this  kinetic  energy  is  manifest  to  us  by 
the  magnetic  forces  which  are  characteristic  of 
a  current.  This  means  that,  if  a  charged  body 
is  given  a  velocity  of  translation,  work  has  to 
be  done  both  in  giving  acceleration  to  the 
material  body  and  in  giving  it  to  the  charge ; 
or,  expressed  differently,  a  charge  of  itself  has 
mass,  inasmuch  as  work  is  required  to  change 
its  motion.  The  question  immediately  arises, 
since  we  have  proved  that  all  material  atoms 
contain  charges,  may  not  the  mass  observed 
in  the  case  of  any  material  body  be  due,  in 
reality,  to  the  charges  contained  by  its  atoms  ? 
If  this  were  true,  we  would  have  an  explana- 
tion of  mass.  One  method  of  testing  this  idea 
is  to  calculate  the  energy  which  a  charge  has  . 
owing  to  its  motion,  and  thus  deduce  its  effec-  I  / 
tive  mass;  then,  knowing  the  charges  asso- 
ciated with  atoms,  we  may  be  able  to  decide 
the  question. 

The  first  to  make  a  calculation  with  this 


64  THE  CONSTITUTION  OF  MATTER 

purpose,  and  the  first  to  propose  this  electrical 
explanation  of  mass  was  J.  J.  Thomson.1  He 
considered  the  motion  of  a  charged  particle, 
and  assumed  that  its  electrical  action  was 
limited  to  the  region  outside  a  minute  sphere 
of  radius  a,  described  around  the  particle  as  a 
center.  Then,  if  the  charge  has  a  value  e,  and 
if  its  velocity  of  translation  is  v,  the  kinetic 
energy  due  to  its  motion  is  found  by  calcu- 

1«2*€2 

lation  to  be  ^--  v*,  provided  the  velocity  is 


not  too  great.  Now,  the  energy  of  translation 
of  a  material  body  of  mass  m  is,  as  we  have 
seen,  %mv*.  It  is  evident,  therefore,  that  the 

2  e2 

"mass"  of  the  charge  is  —  —  .    It  is  impossible 

3  a 

to  compare  this  value  of  the  "  electrical  mass" 
with  that  observed  for  any  charged  body  ow- 
ing to  the  difficulty  of  knowing  the  value  of 
the  distance  a  at  which  we  consider  the  action 


1  See  Phil.  Mag.,  vol.  xi,  p.  227  (1881).  J.  J.  Thomson, 
Electricity  and  Matter  (New  York,  1904);  The  Corpuscular 
Theory  of  Matter  (London,  1907) ;  article  "  Matter,"  Encyc. 
Brit.,  eleventh  edition.  H.  A.  Lorentz,  The  Theory  of  Elec- 
trons (Leipzig,  1909). 


ELECTRIC   MASS  65 

to   begin.   Fortunately,  however,  there   is  a 
method  by  which  the  idea  may  be  tested. 

When  the  calculation  of  the  mass  of  a  mov- 
ing charge  is  made  for  the  case  of  great  veloc- 
ity, it  is  found  that  the  mass  increases  as  the 
velocity  increases ;  and,  assuming  that  the  mass 
of  a  charged  particle  is  due  entirely  to  its 
charge,  Thomson  calculated  the  law  connect- 
ing mass  and  velocity.  An  opportunity  soon 
arose  for  testing  this.  As  you  all  know,  radio- 
active substances,  such  as  radium,  emit  several 
types  of  radiation;  one  of  these,  called  the 
beta  rays,  consists  of  negatively  charged  par- 
ticles, which  are  expelled  with  velocities 
approaching  that  of  light.  These  rays  have 
different  velocities;  and,  by  using  a  method 
devised  by  Thomson,  Kaufmann,  and  later 
Bucherer,1  measured  the  velocities  and  masses 
of  these  particles,  assuming,  as  they  were  jus- 
tified in  doing,  that  the  electric  charge  was 
the  atomic  one.  They  found  that  the  particles 
having  the  greater  velocity  had  the  greater 

1  Ann.  der  Physik,  vol.  xxvm,  p.  513  (1909);  vol.  xxx,  p. 
974  (1909).  See  also  article  by  Wolz,  ibid.,  vol.  xxx,  p.  273 
(1909). 


66  THE   CONSTITUTION  OF  MATTER 

mass,  and  the  connection  between  mass  and 
velocity  was  exactly  what  one  would  expect, 
assuming  that  the  mass  of  the  particle  was  en- 
tirely due  to  its  charge.  This  was  a  most  strik- 
ing result.  Since  the  beta  particles  are  identi- 
cal with  the  corpuscles  which  are  common 
constituents  of  all  atoms,  and  since  their  mass 
is  entirely  electrical  in  origin,  we  can  state 
definitely  that  part  at  least  of  the  mass  of  any 
body  is  due  to  its  corpuscles.  Whether  or  not 
the  entire  mass  is  of  this  electric  origin  will 
depend  upon  the  number  of  corpuscles  present 
in  the  atoms.  Before,  however,  taking  up  this 
point,  I  wish  to  present  to  you  a  different  way 
of  considering  this  question  of  the  mass  of  an 
electric  charge. 

Up  to  this  point  we  have  discussed  simply 
the  total  amount  of  the  mass  of  the  charge 
as  indicated  by  its  kinetic  energy  in  the  sur- 
rounding medium  when  it  is  in  motion.  If  we 
think  of  mass  as  being  given  by  momentum, 
Thomson  has  shown  that  in  reality  this  mass 
is  best  thought  of,  not  as  a  property  of  the 
particle  itself,  but  rather  as  one  of  the  region 


ELECTRIC  MASS  67 

surrounding  the  particle.  This  region  contains 
potential  energy,  as  has  been  said  repeatedly; 
and,  as  the  charged  particle  moves,  it  carries 
with  it  this  energy.  Thomson  proved  that  the 
simplest  way  of  describing  the  mass  of  a 
charged  particle  was  to  assign  a  definite 
amount  of  mass  to  each  element  of  space 
which  contains  potential  energy,  the  one  being 
proportional  to  the  other.  The  exact  statement 
is  that  the  potential  energy  in  any  minute 
volume  equals  J  (electrical  mass  in  that  volume) 
X  (velocity  of  light)2. 

One  must  note  carefully  that  the  momenta 
of  these  minute  elements  of  mass  distributed 
around  the  moving  charged  particle  are  not  in 
general  in  the  same  direction  as  that  of  the 
motion  of  the  particle ;  and  therefore  the  mass 
of  the  charge,  as  shown  by  its  momentum,  is 
not  equal  to  the  sum  of  the  elementary  masses. 
Another  fact  which  must  be  emphasized  is 
that,  inasmuch  as  a  corpuscle  cannot  exist  by 
itself,  but  is  always  associated  with  a  positive 
charge,  even  though  far  separated  from  it, 
this  electrostatic  energy  is  not  to  be  attributed 


68  THE  CONSTITUTION  OF  MATTER 

to  the  corpuscle  alone,  but  to  the  two  equal 
and  opposite  charges.  However,  if  the  cor- 
puscle is  much  smaller  in  volume  than  the 
positive  charge,  the  larger  part  of  the  energy 
is  concentrated  around  it. 

This  association  of  mass  and  potential  energy 
is  perfectly  general  and  holds  for  all  velocities 
of  the  particle,  and  for  every  case  where  there 
is  electrostatic  energy.  An  illustration  of  this 
fact  is  afforded  by  the  effects  of  radiant  energy, 
the  energy  which  is  emitted  by  all  material 
bodies  and  which  is  traversing  space  with  the 
enormous  velocity  of  3  X  1010  centimeters  per 
second.  This  is  in  part  kinetic  and  in  part  po- 
tential. It  has  been  known  for  many  years  that 
it  was  a  consequence  of  the  mathematical 
equations  which  state  our  knowledge  of  elec- 
trical phenomena  and  also  a  consequence  of 
our  theories  concerning  heat-phenomena  that 
radiant  energy  falling  upon  any  body  should 
give  it  a  push  and  that  the  body  emitting  ra- 
diant energy  should  experience  a  recoil.  These 
predictions  of  theory  have  been  verified  by 
direct  experiment.  This  push  and  recoil  are 


ELECTRIC   MASS  69 

of  course  illustrations  of  momentum.  When 
we  calculate  the  mass  as  shown  by  this  light 
pressure  and  compare  it  with  the  amount  of 
potential  energy  in  the  radiation,  it  is  found 
that  there  is  the  same  proportionality  as  in 
the  case  of  the  potential  energy  of  a  charged 
particle.  Further,  Hasenohrl1  has  shown  that, 
if  we  had  a  closed  box  inside  which  radiation 
is  moving  to  and  fro,  the  force  required  to 
produce  a  definite  acceleration  of  the  box  is 
greater  than  it  would  be  if  there  were  no  ra- 
diation, thus  showing  that  the  radiation  pos- 
sesses mass.  One  must  add  that  the  fact  of 
there  always  being  a  definite  mass  associated 
with  a  definite  amount  of  potential  energy, 
regardless  of  whether  the  energy  is  that  of  a 
static  charge  or  is  part  of  radiation  traversing 
space  at  an  enormous  velocity,  is  most  remark- 
able. 

1  Sitz.  Ber.  Wiener  Akad.,  2a.  vol.  cxvi,  p.  1391  (1907); 
vol.  cxvn,  p.  207  (1908).  Comstock  has  shown  (Phil  Mag., 
vol.  xv,  p.  1)  that  "  if  second  order  terms  in  the  velocity  be 
neglected  the  mass  [of  a  purely  electrical  system]  is  a  simple 

constant  -  - 2  multiplied  by  the  total  included  electromag- 
netic energy,"  where  v  is  the  velocity  of  light. 


70          THE  CONSTITUTION  OF  MATTER 

In  all  his  earlier  papers  on  the  subject 
of  the  mass  associated  with  electric  charges, 
Thomson  described  the  phenomena  as  due  to 
the  mass  of  certain  portions  of  the  aether, 
which  he  called  "  bound  aether."  For  many 
purposes  it  is  convenient  to  describe  the  prop- 
erties of  charged  bodies  in  terms  of  what 
Faraday  called  "  lines  of  force."  If  we  con- 
sider a  corpuscle  at  rest,  the  line  of  action  of 
the  force  between  it  and  any  small  positively 
charged  body  in  the  neighborhood  is  the 
straight  line  joining  them ;  and  we  can  asso- 
ciate these  radial  lines,  drawn  from  the  center 
of  the  corpuscle,  with  the  corpuscle  itself, 
calling  them  "lines  of  force."  Most  writers 
have  pictured  the  space  around  any  charged 
conductor  as  filled  with  these  lines,  and  for 
convenience  have  divided  the  space  into  cer- 
tain volumes  bounded  by  the  lines,  thus  forming 
what  may  be  called  "  tubes  of  force."  Thomson, 
on  the  other  hand,  considers  the  tubes  starting 
from  the  charged  conductor  as  of  uniform 
cross-section  throughout  their  entire  length, 
so  that  only  a  small  portion  of  the  space  is 


ELECTRIC  MASS  71 

occupied  by  the  tubes.  He  imagines  a  definite 
amount  of  aether  "  bound  "  to  these  tubes,  so 
that,  if  they  move  lengthwise,  i.e.,  in  the  di- 
rection of  the  tube  itself,  there  is  no  motion 
of  the  aether ;  but,  if  they  move  transversely, 
this  bound  aether  is  carried  along  in  the  motion. 
By  attributing  mass  to  the  aether  it  is  at  once 
evident,  then,  how  we  can  say  that  an  electric 
charge  possesses  mass.  If,  on  the  other  hand, 
we  do  not  postulate  the  existence  of  the  aether, 
but  consider  energy  as  an  entity,  we  keep  all 
of  our  geometry  and  so  do  not  alter  our  men- 
tal picture,  but  simply  change  our  mode  of 
description.  There  are  certain  advantages  in 
Thomson's  earlier  point  of  view,  because  there 
is  a  most  interesting  analogy  which  one  can 
draw  between  the  motion  through  the  aether 
of  a  charged  body  with  its  rod-like  tubes  of 
force  and  that  through  a  fluid  of  a  solid  hav- 
ing long  elastic  pins  stuck  in  it.  Whenever  a 
solid  mass  moves  through  a  fluid,  portions  of 
the  latter  are  set  in  motion  also ;  and  so  the 
apparent  mass  of  the  solid  is  increased,  e.g., 
the  impulse  required  to  bring  to  rest  the  solid 


72  THE   CONSTITUTION  OF  MATTER 

when  moving  through  the  fluid  is  greater  than 
it  would  be  if  the  fluid  were  absent.  Further, 
when  an  oblong-shaped  solid  is  moving  through 
a  fluid,  it  will  turn,  unless  prevented,  so  as  to 
present  its  longer  side  perpendicular  to  the 
line  of  motion.  Thus,  a  falling  leaf  never 
drops  with  its  edge  down,  but  always  flut- 
ters towards  the  earth  with  its  broad  face 
parallel  to  the  earth.  So  in  the  case  of  a  solid 
and  its  pins,  the  latter  will  all  tend  to  place 
themselves  at  right  angles  to  the  line  of  motion. 
As  a  matter  of  fact  the  same  statement  is  true 
of  the  lines  of  force  associated  with  a  moving 
charged  body,  as  was  first  shown  by  Heavi- 
side ;  the  lines  tend  to  collect  into  an  equato- 
rial plane  perpendicular  to  the  line  of  motion  ; 
and  the  increase  in  mass  of  a  charge  when  its 
velocity  becomes  very  great  may  be  shown  to 
be  connected  with  this  change  in  the  geom- 
etry of  the  "  tubes  of  force."  Thomson  has  used 
this  analogy  most  skillfully  in  his  discussion  of 
the  properties  of  moving  charges ;  but  its  use- 
fulness vanishes  if  we  discard  the  conception 
of  the  aether. 


ELECTRIC  MASS  73 

In  considering  the  mass  of  an  electric  charge 
as  distributed  throughout  the  regions  of  space 
where  there  is  electrostatic  energy  owing  to 
the  charge,  we  see  that  strictly  speaking  a 
single  corpuscle  (with  its  complementary  posi- 
tive charge)  produces  mass  throughout  all 
space,  out  to  infinity,  because  its  influence  ex- 
tends that  far,  and  every  portion  of  space  con- 
tains a  certain  amount  of  energy  due  to  it.  If 
there  are  two  corpuscles,  any  element  of 
volume  in  the  surrounding  space  will  contain 
energy  due  to  each  of  them;  and  so  the 
masses  due  to  two  corpuscles  will  occupy  the 
same  space !  The  relative  amounts  of  the  mass, 
though,  in  regions  close  to  and  far  from  a 
corpuscle  may  be  calculated  from  Thomson's 
formula  ;  and  it  is  found  that  practically  all 
of  the  mass  is  concentrated  in  a  region  ex- 
tremely near  the  corpuscle,  less  than  one  mil- 
lionth of  its  mass  being  outside  what  we  may 
call  "  atomic  distance,"  so  we  may  still  picture 
the  corpuscles  as  true  particles,  each  practi- 
cally distinct  from  its  neighbors. 

A  much  more  serious  question  arises,  how- 


74  THE  CONSTITUTION  OF  MATTER 

ever,  when  we  ask  whether  we  can  account  for 
the  entire  mass  of  an  atom  as  due  to  the  elec- 
tric charges  associated  with  it.  I  have  shown 
in  the  first  lecture  that  corpuscles  exist  in  con- 
nection with  the  atoms  of  all  kinds  of  matter, 
and  that  with  every  corpuscle  there  must  be 
associated  an  equivalent  positive  charge.  In 
the  calculation  of  the  mass  of  a  charge,  Thom- 
son assumed  that  the  charge  existed  by  itself, 
that  is,  that  the  equivalent  charge  of  opposite 
sign  was  so  far  removed  as  to  allow  its  influ- 
ence to  be  neglected.  If  this  complementary 
charge  is  in  close  proximity,  however,  to  the 
charged  body,  the  potential  energy  is  decreased, 
and  therefore  so  is  the  electric  mass.  Our  ex- 
periments measure  the  mass  and  charge  of  a 
corpuscle  when  it  is  expelled  from  its  atom ; 
but,  when  it  forms  part  of  the  atom,  and  is 
therefore  associated  with  a  positive  charge, 
the  mass  due  to  the  potential  energy  is  less 
than  that  found  for  the  corpuscle  when  free 
from  the  atom.  The  mass  in  the  latter  case  is 
about  one  eighteen  hundredth  of  that  of  a 
hydrogen  atom ;  let  us  assume,  for  the  sake 


ELECTRIC  MASS  75 

of  having  a  definite  quantity,  that  when  in  a 
hydrogen  atom  the  corpuscle  has  a  mass  one 
two  thousandth  that  of  the  atom.  (The  actual 
value  will  depend  upon  the  number  of  corpus- 
cles, their  distribution,  etc.)  Then,  in  order  to 
account  for  the  total  mass  of  a  hydrogen  atom 
as  due  to  the  potential  energy  of  the  charges, 
we  must  assume  the  existence  in  the  hydrogen 
atom  of  two  thousand  corpuscles.  But,  as  op- 
posed to  this,  stands  the  fact  that  a  great  many 
lines  of  investigation  indicate  clearly  that  a 
hydrogen  atom  has  a  very  small  number  of 
corpuscles,  possibly  not  more  than  three,  and 
that  the  number  of  corpuscles  in  any  atom  is 
proportional  to  its  atomic  weight,  e.g.,  an  oxy- 
gen atom  has  sixteen  times  as  many  as  has  a 
hydrogen  atom,  etc. l  If  this  is  true,  the  mass 
due  to  the  potential  energy  of  the  corpus- 
cles and  the  complementary  positive  charge 
amounts  to  only  a  small  part  of  the  total  mass 
of  the  atom.  It  is  possible,  of  course,  that  the 

1  J.  J.  Thomson,  The  Corpuscular  Theory  of  Matter  (Lon- 
don, 1907) ;  Phil.  Mag.  (vi),  vol.  xxm,  p.  451  (1912).  H.  A. 
Wilson,  Proc.  Amer.  Phil.  Soc.,  vol.  i,p.  371  (1911).  J.  A. 
Crowther,  Proc.  Roy.  Soc.,  vol.  LXXXIV,  p.  226  (1911). 


76  THE  CONSTITUTION  OF  MATTER 

experiments  bearing  upon  the  number  of  cor- 
puscles in  an  atom  are  not  conclusive  ;  it  may 
be  that  they  give  us  knowledge  only  of  cer- 
tain groups  of  corpuscles,  not  of  others.  If, 
however,  we  accept  the  idea  of  a  small  num- 
ber of  corpuscles  in  an  atom,  we  are  forced  to 
the  adoption  of  one  of  two  hypotheses :  — 

(1)  Part  of  the  mass  of  an  atom  is  •  due 
to  mechanical  as  distinct  from  electrical  cau- 
ses. 

(2)  Mass  is  due  to  other  "  electrical "  causes 
than  electrostatic  energy  alone. 

In  this  connection  we  must  note  the  differ- 
ence in  "  size  "  which  Thomson  attributes  to 
the  positive  and  negative  charges  in  an  atom. 
Grant  that  a  hydrogen  atom  has  three  cor- 
puscles; then  the  entire  volume  of  the  atom  is 
considered  as  divided  practically  into  three 
equal  parts,  each  of  which  is  to  be  thought 
of  as  the  volume  of  a  unit  positive  charge. 
Consequently,  the  ultimate  electric  doublet, 
consisting  of  a  corpuscle  and  its  complement- 
ary positive  charge,  form  a  group  of  a  minute 
particle  joined  by  lines  of  force  to  a  rela- 


ELECTRIC  MASS  77 

tively  large  volume.  Thomson  in  speaking  of 
this  has  again  resorted  to  the  analogy  of  a 
solid  moving  through  a  fluid.  If  we  imagine 
a  solid  shaped  like  a  dumb-bell,  but  having 
one  of  the  balls  much  larger  than  the  other, 
it  is  evident  that  in  moving  through  a  fluid 
by  far  the  larger  proportion  of  the  fluid  which 
is  set  in  motion  by  the  solid  is  due  to  the 
larger  ball.  By  way  of  analogy  we  may  com- 
pare the  large  ball  to  the  positive  charge,  the 
small  ball  to  the  negative  one,  and  the  con- 
necting bar  to  the  tube  of  force.  The  nega- 
tive charge  as  such  would  then  not  drag  with 
it  any  aether  practically,  the  tube  of  force 
would  carry  a  little,  that  due  to  the  potential 
energy;  but  the  largest  amount  would  be  as- 
sociated with  the  positive  charge.  Direct  ex- 
perimental evidence  bearing  upon  this  does  not 
exist.  However,  there  is  nothing  in  the  nature 
of  the  idea  of  electrical  mass  or  in  the  concept 
of  a  corpuscle  which  requires  us  to  picture  the 
positive  change  as  having  a  volume  practically 
equivalent  to  that  of  the  atom ;  it  may  be  con- 
centrated into  a  comparatively  small  nucleus 


78          THE  CONSTITUTION  OF  MATTER 

at  the  center  of  the  atom  —  as  has  been  in 
fact  proposed  by  Rutherford. 

I  have  carried  you  in  a  rather  hurried 
manner  through  the  evidence  that  all  atoms, 
no  matter  with  what  element  they  are  associ- 
ated, contain  corpuscles,  i.e.,  atomic  negative 
charges,  and  also  complementary  positive 
charges,  and  have  stated  that  experiments 
point  to  the  idea  that  the  number  of  corpus- 
cles in  an  atom  is  proportional  to  its  atomic 
weight.  Expressed  differently,  this  means  that 
the  mass  of  any  atom  is  proportional  to  the 
number  of  corpuscles  it  contains. 

In  the  remaining  part  of  this  lecture  I  wish 
to  describe  in  some  detail  the  experiments 
upon  which  our  knowledge  rests. 

One  of  the  most  important  facts  upon  which 
the  theory  is  based  is  that  there  is  an  atomic 
electric  charge,  which  is  always  associated 
with  a  corpuscle.  This  means  that  there  is  a 
definite  charge  so  small  that  none  smaller  has 
been  observed,  and  such  that  all  charges 
measured  are  either  equal  to  this  or  multiples 
of  it.  This  concept  of  an  atomic  charge  is  due 


PROPERTIES  OF  CORPUSCLES  79 

to  Faraday  and  was  used  by  him  to  describe 
the  phenomena  of  conduction  of  an  electric 
current  by  a  solution  of  salt  or  acid  in  water. 
The  idea  of  its  extension  to  all  charges  is  due 
to  J.  J.  Thomson ;  and  he  was  the  first  to 
prove  that  there  was  an  atomic  charge  on  a 
corpuscle,  equal  to  that  observed  in  Faraday's 
experiments.  His  work  on  this  point,  although 
the  earliest,  is  not  the  best,  as  later  experi- 
menters have  improved  his  methods.  The 
most  interesting  investigation  on  the  subject, 
in  view  of  the  theoretical  simplicity  of  the  ob- 
servations and  the  clearness  of  the  conclu- 
sions, is  the  one  carried  through  in  such  a 
masterly  manner  by  Professor  Millikan,  of  the 
University  of  Chicago.1  In  devising  his  method 
he  took  advantage  of  the  following  well- 
known  facts : — 

(1)  A  minute  drop  of  oil  or  mercury  or  any 
liquid  will  fall  under  the  influence  of  gravity 
at  a  rate  depending  upon  its  properties  and 
those  of  the  surrounding  gas.  (The  laws  for 

1  Popular  Science  Monthly,  April,  1912  ;  Physical  Review, 
vol.  XXXH,  p.  349  (1911)  ;  February,  1913. 


80  THE  CONSTITUTION  OF  MATTER 

this  fall  have  been  investigated  by  Stokes,  by 
Cunningham,  and  by  Millikan  himself.) 

(2)  It  is  possible  by  various  means  to  add  a 
charge  to  these  drops;  and  therefore,  by  ap- 
plying an  electric  force  in  a  vertical  direction, 
one  can  neutralize  this  falling  of  a  drop  or 
reverse  its  motion. 

In  the  actual  experiments  a  single  charged 
drop  was  isolated  and  carefully  watched;  it 
fell  through  a  known  distance,  the  time  being 
noted ;  an  electric  field  of  known  intensity  was 
applied  so  as  to  reverse  its  motion  and  the 
time  of  rise  was  observed;  it  was  again  al- 
lowed to  fall,  etc.  The  formulae  which  apply 
to  these  conditions  lead  at  once  to  a  value  for 
the  charge  carried  by  the  drop ;  and  Millikan's 
observations  prove  beyond  any  shadow  of 
doubt  that  this  charge  is  of  an  atomic  nature. 
The  value  obtained  for  the  atomic  charge  was 
4.774  X 10-10  electrostatic  units,  or  1.591  X  lO'20 
when  expressed  in  the  "  electromagnetic  sys- 
tem." In  these  experiments  some  drops  were 
charged  positively,  some  negatively;  some 
had  a  unit  charge ;  others,  multiples  of  this. 


PROPERTIES  OF  CORPUSCLES      81 

The  correctness  of  his  method  has  been  ques- 
tioned ;  but  he  has  shown  to  the  satisfaction 
of  all  that  the  criticisms  are  not  well  founded. 
When  considered  in  all  its  aspects  this  inves- 
tigation by  Professor  Millikan  may  be  con- 
sidered one  of  the  most  brilliant  ever  carried 
on  in  this  country. 

The  value  of  the  atomic  charge  carried  in 
experiments  like  those  of  Faraday  cannot  be 
determined  directly ;  but  the  ratio  of  this  to 
the  mass  of  the  particle  carrying  the  charge 
may  be.  This  is  9648.9,  when  the  carrier  of 
the  charge  is  a  hydrogen  atom,  using  the 
electromagnetic  system  of  units.  The  fact  that 
Faraday's  atomic  charge  is  identical  with  the 
corpuscular  charge  was  proved  by  Townsend 
and  also  by  H.  A.  Wilson  ;  and  therefore 
knowing  this  charge  to  be  1.59  XlO20,  it  fol- 
lows that  the  mass  of  a  hydrogen  atom  is 
1.65X10'24  grams.  From  a  knowledge  of 
this  mass  and  the  atomic  weights,  we  can  cal- 
culate at  once  the  mass  of  the  atom  of  any 
element. 

It  is  well  known  from  experiments  on  the 


82  THE  CONSTITUTION   OF  MATTER 

liberation  of  hydrogen  gas  by  passing  an  elec- 
tric current  through  solutions  of  acid  in  water 
that  one  electromagnetic  unit  of  charge  liber- 
ates 1.1657  cubic  centimeters  of  the  gas.  Each 
molecule  of  the  gas  has  been  formed  out  of 
two  atoms,  each  of  which  carries  the  atomic 
charge ;  therefore,  if  there  are  JVmolecules  in 
each  cubic  centimeter  of  the  gas,  the  total 
charge  carried  must  be  2^X1.1657  X  1.59 
X  lO"20.  But  this  must  equal  1.  Hence  we  can 
calculate,  N=2.7 XlO19.  (This  is  the  number 
of  molecules  per  cubic  centimeter  of  any  gas 
at  0°  C  and  at  normal  barometric  pressure.) 
To  give  an  idea  of  the  enormous  magnitude 
of  this  number,  Thomson  calls  attention  to 
the  fact  that,  if  a  person  were  to  count  and 
collect  molecules  at  the  rate  of  one  per  second 
for  one  hundred  million  years,  he  would  not 
have  sufficient  for  chemical  detection. 

In  order  to  determine  the  mass  of  the  cor- 
puscle, Thomson  made  use  of  a  most  ingen- 
ious method.  If  a  charged  body  is  moving 
rapidly,  it  has,  as  has  been  stated  before,  both 
an  electric  and  a  magnetic  field ;  so  it  will  be 


PROPERTIES  OF  CORPUSCLES  83 

acted  on  itself  by  both  electric  and  magnetic 
forces.  Under  the  action  of  either  one  the 
path  of  the  moving  charge  would  be  deflected ; 
and  therefore,  by  choosing  suitable  forces  of 
the  two  types,  we  may  make  one  neutralize 
the  effect  of  the  other,  as  will  be  shown  by 
the  path  of  the  particle  remaining  unchanged. 
When  the  proper  formulae  are  applied  to  this 
condition,  it  is  found  that  we  can  determine 
the  velocity  of  the  moving  charge  and  the 
ratio  of  its  charge  to  its  mass,  if  we  measure 
the  two  balancing  forces.  When  this  method 
is  used  with  the  particles  constituting  the 
cathode  rays,  and  with  those  emitted  by  hot 
bodies  or  by  bodies  under  the  action  of  light, 
it  is  found  that,  although  the  velocities  may 
vary  greatly,  the  ratio  of  charge  to  mass 
is  the  same  for  them  all,1  its  value  being 
1.77  X 107.  Knowing  the  value  of  the  charge, 
the  value  of  the  mass  is  thus  seen  to  be 
9.00  X  10~28,  which  is  about  one  eighteen  hun- 
dredth of  that  of  the  hydrogen  atom.  It  was 

1  See  article  by  Wolz,  Ann.  der  Physik,  vol.  xxx,  p.  273 
(1909).  The  value  adopted  by  him  is  1.7674  X  107. 


84  THE  CONSTITUTION  OF  MATTER 

by  simple  modifications  of  Thomson's  method 
that  the  properties  of  the  beta  rays  emitted 
by  radium  and  other  radio-active  bodies  were 
studied,  and  that  it  was  proved  that,  as  the 
velocity  of  the  particles  becomes  very  great, 
the  mass  increases.  (This  interpretation  is,  of 
course,  based  upon  the  assumption  that  the 
value  of  the  electric  charge  remains  un- 
changed; but  there  is  no  reason  for  doubt- 
ing this.) 

When  it  comes  to  the  question  of  the  charge 
and  mass  of  the  elementary  positive  particles, 
there  are  two  investigations  which  must  be 
mentioned.  The  first  of  these  is  that  by  Thom- 
son upon  the  nature  of  the  canal  rays  in  vac- 
uum tubes,  to  which  brief  reference  has  been 
made  before.  He  determined  by  the  method 
just  described  the  velocity  and  the  ratio  of 
charge  to  mass  of  the  particles  constituting 
these  rays,  and  found,  in  the  case  of  any  def- 
inite gas,  that  there  were  carriers  of  different 
masses  ;  one  corresponded  always  to  a  hydro- 
gen atom  no  matter  what  the  gas  was.  The 
other  investigation  was  a  most  wonderful 


PROPERTIES  OF  CORPUSCLES      85 

'~Hf 

series  of  experiments  concerning  the  proper- 
ties of  radium,  made  by  Rutherford  and  his 
associates.  As  has  been  said  before,  radium 
emits  corpuscles  and  also  positively  charged 
particles  of  much  larger  mass,  which  are  called 
alpha  particles.  Geiger  and  Rutherford  de- 
vised two  methods  by  which  the  actual  num- 
ber of  alpha  particles  emitted  per  second  by  a 
given  mass  of  radium  may  be  counted,  and 
proved  that  these  were  charged  helium  atoms. 
Then,  knowing  from  the  application  of  Thom- 
son's method,  the  ratio  of  the  charge  to  the 
mass  of  each  particle,  it  was  shown  that  each 
particle  carried  a  double  atomic  charge.1 

I  cannot  pass  by  these  brilliant  experiments 
without  calling  your  special  attention  to  at 
least  one  other  feature.  Since  the  foundation 
of  modern  science  people  have  believed  in  the 
existence  of  molecules  and  atoms,  but  who 
has  had  hope  of  ever  securing  any  knowl- 

1  Rutherford  and  Geiger,  Proc.  Roy.  Soc.,  vol.  LXXXI, 
pp.  141  and  162  (1908).  Regener,  Sitz.  Ber.  Berlin  Akad., 
vol.  xxxvni,  p.  948  (1909).  Geiger  and  Rutherford  have 
also  counted  the  alpha  particles  emitted  by  uranium  and 
thorium  :  Phil.  Mag.,  vol.  xx,  p.  691  (1910).  See  also  Phil. 
Mag.,  vol.  xxiv,  p.  618  (1912). 


86          THE  CONSTITUTION  OF  MATTER 

edge  of  an  individual  atom?  Its  size  is  so  ex- 
traordinarily minute  and  its  mass  so  far  be- 
yond the  power  of  any  balance  to  recognize, 
even  granting  the  possibility  of  isolating  it. 
But,  here,  in  the  experiments  of  Kutherford 
we  can  actually  count  the  atoms  of  helium  as 
they  are  ejected  from  the  parent  radium.  The 
property  of  the  atom  which  is  made  use  of 
is  not  its  size  nor  its  mass,  but  its  velocity  of 
motion.  When  a  charged  particle  moves  with 
sufficient  speed  through  a  gas,  the  latter  is 
ionized,  becoming  a  good  electric  conductor ; 
and  this  fact  may  be  easily  recognized  by  the 
use  of  well  -  known  electrical  instruments. 
(The  method  is  not  unlike  one  that  might  be 
used  in  counting  the  number  of  bullets  fired 
from  a  gun  by  observing  the  holes  made  in  a 
target.)  Again,  when  an  alpha  particle  strikes 
certain  phosphorescent  substances,  such  as 
Sidot's  blende,  there  is  a  brilliant  instantane- 
ous emission  of  light,  which  is  called  a  "  scin- 
tillation." Taking  advantage  of  these  facts, 
Rutherford  was  able  actually  to  count  the  in- 
dividual atoms.  His  experiments  showed  that 


PROPERTIES  OF  CORPUSCLES  87 

one  gram  of  radium  emits  3.4  X 1010  alpha 
particles  each  second,  and  that  each  particle 
carries  3.1  X 10'20  electromagnetic  charge. 
Since  each  particle  carries  a  double  atomic 
charge,  this  gives  for  that  quantity  the  value 
1.55  X  10~20  which  is  in  close  agreement  with 
the  value  given  by  Millikan,  viz.,  1.59  XlO"20. 
In  deducing  the  value  of  the  mass  of  a  cor- 
puscle it  is  evident  that  some  assumption  must 
be  made  in  regard  to  the  space  occupied  by  it. 
Some  authors  have  considered  the  charge  dis- 
tributed over  the  surface  of  a  conducting 
sphere;  others,  as  distributed  uniformly 
through  the  volume  of  a  non-conducting 
sphere.  It  is  difficult  to  say  what  meaning,  if 
any,  these  words — conducting  and  non-con- 
ducting—  would  have  in  speaking  of  a  cor- 
puscle ;  and,  as  a  matter  of  fact,  the  formulae 
deduced  are  all  the  same  provided  the  velocity 
of  motion  of  the  charged  body  is  not  too  great. 
In  deducing  his  original  formula  for  the  mass 
of  a  charge,  Thomson  assumed  that  the  action 
was  the  same  as  if  the  charge  were  concen- 
trated at  a  point  and  that  the  force  began  at 


88  THE  CONSTITUTION  OF  MATTER 

an  arbitrary  distance  from  this  point.  Under 
these  conditions,  if  we  call  a  this  distance,  it 
is  not  difficult  to  prove  that  the  formula  con- 
necting mass  and  charge  is 

2e* 

m  =  ~- 
o  a 

Having  by  experiments  on  the  corpuscle  de- 
termined its  mass  and  charge,  we  may  substi- 
tute these  values  in  this  formula,  and  thus  ob- 
tain the  value  of  a,  i.e.,  the  radius  of  the 
"sphere  of  action"  of  the  corpuscle.  This  is 
found  to  be  2  X  lO'13  cm. 

When  we  discuss  rigidly  the  mass  of  a 
charged  body  having  a  great  velocity,  we  can- 
not shirk  the  question  as  to  the  distribution 
of  the  charge ;  because  we  find  that  the  value 
deduced  for  the  mass  depends  upon  our  as- 
sumptions. Lorentz,  who  has  been  most  suc- 
cessful in  solving  this  problem,  has  deduced  a 
formula,  which,  so  far  as  experimental  evi- 
dence at  present  goes,  has  been  verified.  He 
assumes  that  the  charge  of  the  corpuscle  may 
be  considered  distributed  over  a  conducting 
surface  which  at  small  velocities  is  a  sphere, 


PROPERTIES   OF  CORPUSCLES  89 

but  at  great  velocities  becomes  flattened  into 
an  ellipsoid  having  its  broader  face  at  right 
angles  to  the  motion.1 

1  H.  A.Lorentz,  The  Theory  of  Electrons  (Leipzig,  1909). 


Ill 

RADIO-ACTIVITY ;  GRAVITATION 

EVERY  one  in  the  audience  remembers,  doubt- 
less, the  great  interest,  almost  excitement, 
aroused  by  the  discovery  of  the  Roentgen 
rays  in  1895.  There  certainly  was  a  great 
deal  that  was  spectacular  in  their  properties; 
but  from  the  standpoint  of  addition  to  knowl- 
edge, the  most  important  consequence  of  their 
discovery  was  an  indirect  one.  You  may  re- 
member that  the  seat  of  production  of  the 
Eoentgen  rays  is  the  solid  obstacle  which  stops 
the  cathode  rays  in  a  vacuum  tube ;  and  that 
in  the  original  experiments  of  Roentgen,  this 
obstacle  was  a  portion  of  the  glass  wall  of  the 
tube.  A  conspicuous  fact  in  any  vacuum  tube 
is  the  brilliant  luminescence  of  the  glass  wall 
where  struck  by  the  cathode  rays ;  so  in  these 
experiments  we  have  the  glass  wall  exhibiting 
two  phenomena :  it  is  emitting  light  under  the 
stimulation  of  the  impacts  of  the  cathode  par- 


RADIO-ACTIVITY  91 

tides  and  it  is  the  source  of  the  Roentgen 
rays.  The  idea  occurred  to  the  French  physi- 
cist, Henri  Becquerel,  to  investigate  the  pos- 
sibility of  there  being  a  similar  emission  of 
Roentgen  rays  when  a  body  is  emitting  light 
under  what  we  may  call  artificial  stimulation. 
The  salts  of  uranium  have  been  known  for 
some  time  to  have  the  property  of  continuing 
to  emit  light  after  having  been  exposed  to 
light.  (Bodies  having  this  property  are  said  to 
be  "  phosphorescent.")  Becquerel,  then,  having 
exposed  some  uranium  salts  to  light,  carried 
on  a  series  of  researches  to  see  if  they  emitted 
any  other  radiation  than  light.  He  found  that 
they  did ;  but  that  the  new  radiation  was  dif- 
ferent in  essential  respects  from  Roentgen 
rays.  This  was  the  primary  discovery  in  the 
field  of  what  is  now  called  radio-activity.1 
Owing  to  the  investigations  of  Becquerel,  of 
the  two  Curies,  —  husband  and  wife,  —  of 
Rutherford,  of  Boltwood  in  this  country,  and 

1  Rutherford,  Radio- Activity  (1905);  Radio-Active  Trans- 
formations (1906);  Radio-Active  Substances  and  their  Radia- 
tions (1913).  Madame  Curie,  Traite  de  Radio  activite,2  vols. 
(1910).  Jahrbuch  der  Radioaktivitat  und  Elektionik. 


92  THE  CONSTITUTION  OF  MATTER 

many  others  inspired  by  them,  the  science 
of  radio-activity  now  rests  upon  a  founda- 
tion of  well-established  facts  and  inspiring 
theory. 

Several  other  substances  have  been  found 
occurring  in  natural  ores  which  have  the  prop- 
erty of  radio-activity;  the  two  best  known  are 
radium  and  thorium.  All  of  these  are  charac- 
terized by  the  spontaneous  emission  of  several 
types  of  radiation,  which  have  received  the 
names  alpha,  beta,  and  gamma  rays.  The  alpha 
rays  are  atoms  of  helium,  each  carrying  a  pos- 
itive double  atomic  charge;  the  beta  rays  are 
corpuscles;  the  gamma  rays  are  in  all  proba- 
bility identical  with  a  certain  type  of  Roent- 
gen rays,  being  a  form  of  radiant  energy. 
Rutherford  advanced  the  accepted  theory  of 
these  phenomena,  and  has  by  his  own  investi- 
gations contributed  largely  to  its  proof.  The 
fundamental  idea  is  that,  being  given  a  radio- 
active substance,  a  certain  number  of  its  atoms 
are  undergoing  a  transformation  into  a  differ- 
ent type  of  atom,  the  transformation  consist- 
ing in  the  emission  of  the  rays  and  in  the 


RADIO-ACTIVITY  93 

rearrangement  of  the  remaining  parts  of  the 
atom.  Thus,  we  picture  such  an  atom  as  being 
made  up  of  parts  and  as  becoming  unstable 
owing  to  certain  causes ;  it  then  "  breaks  down  " 
and  some  of  the  constituent  parts  are  ejected ; 
the  remaining  parts  rearrange  themselves,  form- 
ing a  new  atom ;  if  this  new  atom  then  becomes 
unstable,  it  may  break  down,  ejecting  parti- 
cles, and  permitting  another  atom  to  form; 
etc.  It  is  important  to  note  that  this  instabil- 
ity of  the  atom  does  not  depend  upon  its  age 
or  upon  any  known  physical  condition ;  and 
therefore  it  is  hardly  correct  to  speak  of  the 
atom  "becoming  unstable.  By  his  investigations 
Kutherford  has  proved  that  this  hypothesis  of 
radio-active  transformation  accounts  for  the 
observed  facts.  In  certain  steps  an  alpha  par- 
ticle is  emitted ;  in  others  a  beta  particle ;  and 
in  a  few  there  is  no  emission  but  simply  an 
internal  rearrangement  of  the  parts.  It  has 
been  shown  very  recently  that  a  certain  pro- 
portion of  atoms  of  a  definite  kind  may  lose 
an  alpha  particle,  while  the  rest  of  these 
atoms  lose  a  beta  particle;  thus  one  type 


94  THE  CONSTITUTION  OF  MATTER 

of  atom  gives  rise  directly  to  two  different 
kinds.1 

By  the  very  recent  work2  of  Dr.  Gray  and 
Sir  William  Ramsay  certain  features  of  this 
theory  have  been  proved  conclusively  by  quan- 
titative measurements.  They  perfected  a  bal- 
ance capable  of  detecting  a  change  of  the 
weights  in  the  balance-pans  of  one  hundred 
thousandth  of  a  milligram,  a  marvelous  exhi- 
bition of  experimental  skill.  By  means  of  this 
they  succeeded  in  measuring  the  atomic  weight 
of  radium  emanation,  which  according  to  the 
theory  is  formed  from  radium  by  the  emission 
of  an  alpha  particle.  The  atomic  weight  of 
radium  is  known  to  be  226.4,  that  of  an  alpha 
particle  is  4 ;  and  therefore  by  Rutherford's 
theory  the  atomic  weight  of  the  radium  ema- 
nation should  be  226.4-4,  or  222.4.  These 
investigators  determined  it  to  be  223,  which 
is  a  wonderful  agreement  when  one  considers 
the  difficulties  of  the  research. 

1  Physik.  Zeitsch.,  p.  369  (1911);  pp.  623,  699  (1912). 
Proc.  Phys.  Soc.  of  London,  vol.  xxiv,  p.  50  (1911). 

2  Proc.  Roy.  Soc.,  vol.  LXXXIV,  p.  536  (1911). 


RADIO-ACTIVITY  95 

The  facts  so  far  as  they  are  known  to-day, 
are  that  a 

Uranium  atom  loses  an  alpha  particle,  becoming  a 
Uranium2  atom  ;  *  this  loses  an  alpha  particle,  becoming  a 
Uranium  X  atom ;  this  loses  a  beta  particle,  becoming  an 
Ionium  atom ;  this  loses  an  alpha  particle,  becoming  a 
Radium  atom  ;  this  loses  an  alpha  and  a  beta  *  particle 

becoming  a 
Radium  emanation  atom ;  this  loses  an  alpha  particle, 

becoming  a 

Radium  A  atom ;  this  loses  an  alpha  particle  becoming  a 
Radium  B  atom  ;  this  loses  a  beta  particle,  becoming  a 
Radium  C  atom ;  this  loses  an  alpha  and  a  beta  particle, 

becoming  a 

Radium  D  atom ;  this  loses  a  beta2  particle,  becoming  a 
Radium  E  atom  ;  this  loses  a  beta  particle,  becoming  a 
Radium  F  (Polonium)  atom ;  this  loses  an  alpha  parti- 
cle, becoming  a  Lead  atom. 

A  very  small  proportion  of  Radium  C  atoms  form  what 
are  called  Radium  C2  atoms ;  these  lose  beta  parti- 
cles, etc. 

By  some  process,  at  present  unknown,  a  Uranium  atom 
gives  rise  to  an  Actinium  atom ;  it  transforms  into  a 

Radio-actinium  atom ;  this  loses  an  alpha  and  a  beta 
particle,  becoming  an 

1  Madame  Curie  calls  the  intermediate  product  between 
Uranium  and  Uranium  X  Radiouranium.  A  small  portion 
of  the  Uranium2  atoms  form  by  disintegration  a  different 
atom  from  Uranium  X  ;  this  has  been  called  Uranium  Y. 

2  These  beta  particles  are  corpuscles  having  a  compara- 
tively slow  velocity. 


96  THE  CONSTITUTION  OF  MATTER 

Actinium  X  atom ;  this  loses  an  alpha  particle,  becom- 
ing an 

Actinium  emanation  atom  ;  this  loses  an  alpha  particle, 
becoming  an 

Actinium  A  atom ;  this  loses  an  alpha  particle,  becom- 
ing an 

Actinium  B  atom ;  this  loses  a  beta  particle,  becoming  an 

Actinium  C  atom ;  this  loses  an  alpha  particle,  becom- 
ing an 

Actinium  D  atom ;  this  loses  a  beta  particle. 

A  Thorium  atom  loses  an  alpha  particle  and  becomes  a 
Mesothorium  I  atom  ;  this  transforms  into  a 
Mesothorium  II  atom ;  this  loses  a  beta  particle,  becom- 
ing a 

Eadiothorium  atom ;  this  loses  an  alpha  particle,  becom- 
ing a 

Thorium  X  atom ;  this  loses  an  alpha  and  a  beta  parti- 
cle, becoming  a 
Thorium  emanation  atom ;  this  loses  an  alpha  particle, 

becoming  a 

Thorium  A  atom  ;  this  loses  an  alpha  particle,  becoming  a 
Thorium  B  atom  ;  this  loses  a  beta  particle,  becoming  a 
Thorium  C  atom ;  this  loses  an  alpha  particle,  becoming  a 
Thorium  D  atom ;  this  loses  a  beta  particle.  . 

Some  of  the  Thorium  C  atoms  lose  beta  particles,  be- 
coming what  are  called  Thorium  C2  atoms;  these 
lose  alpha  particles,  etc. 

It  is  thus  seen  that  several  well-known  ele- 
ments owe  their  origin  to  the  disintegration 
of  the  atoms  of  other  elements,  and  there  are 


RADIO-ACTIVITY  97 

now  known  over  thirty  radio-active  atoms. 
Some  appear  as  solids,  others  as  gases.  Fur- 
ther it  should  be  noted  that,  if  we  allow  these 
radio-active  transformations  to  go  on  inside  a 
closed  space,  there  is  a  gradual  accumulation 
of  helium  gas.  This  is  due  to  the  fact  that  the 
alpha  particles  are  helium  atoms ;  and  these 
become  the  ordinary  gaseous  molecules  as  soon 
as  they  become  electrically  neutral  by  attaching 
corpuscles  to  themselves.  Rutherford  proved 
this  conclusively  by  allowing  alpha  particles 
to  penetrate  by  impact  into  a  tube  having 
very  thin  walls,  and  then  showing  that  helium 
gas  collects  in  the  tube.1  This  gas  is  a  so-called 
non-atomic  one ;  i.e.,  each  of  its  molecules  con- 
sists of  simply  one  atom.  It  is  most  easily  de- 
tected by  the  character  of  light-radiation  it 
emits  when  an  electric  discharge  is  passed 
through  it. 

The  time  required  for  a  definite  proportion 
of  a  given  quantity  of  any  one  of  the  radio- 
active atoms  to  break  down  into  the  next  atom 

1  Rutherford  and  Royds,  CJiem.  News,  vol.  xcix,  p.  49 
(1909)  ;  Phil.  Mag.,  vol.  xvn,  p.  281  (1909).  See  also  Bolt- 
wood  and  Rutherford,  Phil.  Mag.,  vol.  xxii,  p.  586  (1911). 


98  THE  CONSTITUTION  OF  MATTER 

in  the  series  is  perfectly  characteristic  of  the 
change,  and  has  been  measured  with  a  marked 
degree  of  accuracy.  This  time-element  is  gen- 
erally given  as  the  number  of  seconds,  min- 
utes, or  years  required  for  one  half  of  the 
atoms  to  be  transformed.  It  varies  from  one 
five  hundredth  of  a  second  in  the  case  of 
Actinium  A  to  five  billion  years  for  Uranium. 
The  law  obeyed  is  that  characteristic  of  a  the- 
ory of  probability,  and  offers  no  suggestion  as 
to  an  explanation. 

With  reference  to  the  special  subject  of 
this  course  two  facts  stand  out  with  clearness : 
one  is  that  here  we  have  plain  evidence  of  a 
simple  connection  between  atoms  of  different 
elements ;  the  other  is  that  the  potential  energy 
of  a  radio-active  atom  is  being  decreased  by 
the  emission  of  the  various  types  of  radiation. 
(For  the  sake  of  analogy  we  can  think  of  a 
coiled  spring  and  bullet  such  as  constitute  a 
toy  gun  ;  the  compressed  spring  has  potential 
energy,  the  bullet  when  expelled  gains  kinetic 
energy  at  the  expense  of  the  loss  of  potential 
energy  by  the  spring.) 


GRAVITATION  99 

Therefore  in  proposing  any  general  scheme 
for  the  constitution  of  an  atom,  these  facts  in 
regard  to  radio-active  transformations  are  of 
the  utmost  importance ;  and,  inasmuch  as  we 
have  here  definite  and  known  losses  of  poten- 
tial energy,  we  can  test  certain  of  our  ideas 
concerning  weight  and  mass,  so  far  as  the  lat- 
ter is  due  to  electrical  causes. 

Weight  is  the  second  fundamental  property 
of  matter,  which  I  mentioned  in  the  first  lec- 
ture. We  speak  of  a  body  as  "  heavy "  or 
"  light,"  meaning  to  convey  the  idea  of  the 
intensity  of  stimulation  of  our  muscle-senses 
when  we  keep  the  body  from  falling  towards 
the  earth  by  suspending  it  in  our  hand  or  on 
our  back.  This  means  that  there  is  a  force  act- 
ing between  the  suspended  body  and  the  earth ; 
and  to  this  force  we  give  the  name  "  weight." 
Newton  made  the  hypothesis  that  there  was  a 
similar  force  between  any  two  material  bodies, 
and  proposed  a  law  for  its  action,  which  is  known 
as  Newton's  "  Law  of  Gravitation."  It  may  be 
expressed  as  follows :  let  us  consider  two  parti- 
cles of  matter  whose  masses  are  known  quan- 


100        THE  CONSTITUTION  OF  MATTER 

titles,  mi  and  ^2?  and  whose  distance  apart  is 
r,  then  there  is  a  force  between  them  propor- 
tional to  the  product  of  the  values  of  the 
masses  and  inversely  to  the  square  of  the  value 
of  the  distance.  The  real  importance  of  this 
statement  or  hypothesis  lies  as  much  in  what 
is  omitted  purposely  as  in  what  is  said  explic- 
itly ;  for,  in  order  to  make  the  law  complete, 
we  must  add  :  this  force  of  attraction  is  inde- 
pendent of  the  nature  or  condition  of  the 
bodies,  i.e.,  whether  they  are  solid  or  not, 
whether  they  are  hot  or  cold,  whether  they 
are  made  of  one  element  or  another  or  any 
combination  of  elements ;  it  is  independent  of 
the  medium  surrounding  the  bodies  or  sepa- 
rating them.  In  other  words,  the  only  elemen- 
tary ideas  involved  in  gravitation  are  the  masses 
of  the  parts  concerned  and  their  distance  apart, 
a  most  remarkable  fact,  if  true. 

In  order  to  see  if  this  hypothesis  of  his  did 
truly  describe  the  phenomena  of  nature,  New- 
ton proceeded  to  make  some  experiments  of  his 
own,  and  also  drew  various  deductions  from 
it  so  as  to  compare  them  with  known  facts 


GRAVITATION 


101 


of  astronomy.  His  first  difficulty  was  a  mathe- 
matical one.  The  hypothesis  as  made  applies 
to  two  particles,  i.e.,  to  portions  of  matter  oc- 
cupying such  minute  volumes  that  we  can 
neglect  their  dimensions  in  comparison  with 
their  distance  from  each  other ;  but  if  it  is  to 
be  applied  to  observations  on  large  bodies, 
such  as  any  we  actually  work  with  or  any  of  the 
astronomical  bodies,  a  mathematical  calcula- 
tion must  first  be  made  as  to  how  such  an 
extended  body  would  act,  assuming  that  it 
may  be  considered  made  up  out  of  particles. 
This  calculation  is  comparatively  easy,  given 
the  distribution  of  the  matter  in  space,  pro- 
vided we  have  a  knowledge  of  what  is  called  the 
"  infinitesimal  calculus,"  a  branch  of  mathe- 
matics which  Newton  himself  elaborated, 
partly  for  the  purpose  of  which  we  are  speak- 
ing. He  succeeded  in  convincing  himself  that 
for  all  points  outside  a  spherical  portion  of 
homogeneous  matter  the  action  was  the  same 
as  it  would  be  if  all  the  matter  were  concen- 
trated at  the  center,  and  that  the  same  is  true 
of  any  homogeneous  shell  inclosed  between 


102        THE   CONSTITUTION  OF  MATTER 

two  concentric  spherical  surfaces.  He  assumed, 
therefore,  that,  as  a  first  approximation  to 
the  actual  fact,  any  of  the  astronomical  bodies 
could  be  treated  mathematically  as  a  particle 
concentrated  at  its  center ;  he  deduced  the  con- 
sequences, and  then  compared  them  with  the 
observations  which  were  available.  Let  me  give 
a  resume  of  these.  Copernicus  had  convinced 
most  people  that  the  sun  and  planets  formed 
a  system  of  which  the  former  was  the  center 
around  which  the  latter,  including  the  earth, 
were  moving  in  fixed  orbits.  In  order  to  test 
this  theory  many  new  observations  were  made, 
especially  by  Tycho  Brahe,  whose  observatory, 
established  at  Uraniberg  on  Huena,  a  small 
island  belonging  to  Denmark,  was  equipped 
with  the  best  instruments  available  at  that 
time  at  the  expense  of  King  Ferdinand  II 
of  Denmark.  These  observations  of  Tycho 
Brahe' s  continued  for  many  years,  and  were 
more  accurate  than  any  others  made  before 
that  time.  Towards  the  end  of  his  life  Tycho 
Brahe  lived  in  Prague ;  and  among  his  assist- 
ants was  a  young  German  named  Johann  Kep- 


GRAVITATION  103 

ler.  After  Tycho  Brahe's  death,  the  latter 
fell  heir  to  his  records  and  observations ;  and 
he  spent  the  rest  of  his  life  in  studying  them. 
After  many  fruitless  attempts  he  succeeded  in 
proving  that  all  of  Tycho  Brahe's  observa- 
tions could  be  described  by  three  simple  state- 
ments, which  have  since  been  called  "  Kepler's 
Laws."  If  Newton's  hypothesis  as  to  the  inter- 
action of  material  bodies  is  correct,  and  if 
gravitation  is  the  determining  cause  of  the  as- 
tronomical motions,  then  Kepler's  laws  must 
be  mathematical  consequences  of  this  hypoth- 
esis. This  Newton  showed  to  be  the  case,  a 
most  wonderful  achievement.  He  observed, 
further,  that  another  test  of  his  hypothesis  was 
afforded  by  a  comparison  of  the  motion  of  the 
moon  in  its  orbit  around  the  earth  and  that  of 
a  body  falling  to  the  earth  from  a  point  close 
to  it.  If  it  were  not  for  the  gravitational  ac- 
tion of  the  earth  upon  the  moon,  the  latter 
would  not  move  in  its  approximately  circular 
orbit,  but  would  fly  off  tangentially.  If  we 
know  the  radius  of  the  moon's  orbit  and  its 
period  of  revolution,  we  can  deduce  the  dis- 


104        THE  CONSTITUTION  OF  MATTER 

tance  it  "  falls  in  "  towards  the  earth  each  unit 
of  time;  the  distance  an  ordinary  falling  body 
close  to  the  earth's  surface  falls  toward  it  in 
a  unit  of  time  may  be  deduced  from  observa- 
tions upon  pendulums;  in  accordance  with 
Newton's  law  the  effect  of  gravity  at  the  earth's 
surface  should  be  60  x  60,  or  3600,  times  as 
great  as  that  at  the  center  of  the  moon,  be- 
cause the  distance  from  the  center  of  the  earth 
to  that  of  the  moon  is  sixty  times  that  from 
the  center  of  the  earth  to  its  surface.  Newton 
was  able  to  find  among  astronomical  records 
the  figures  he  needed  for  the  calculation  of 
the  moon's  motion;  and  he  used  Huyghens's 
pendulum  observations  in  order  to  deduce  the 
gravitational  force  of  the  earth  at  a  point  on 
its  surface.  When  he  made  his  calculations  he 
found  his  law  verified  to  a  high  degree  of 
accuracy. 

Before  continuing  the  discussion  of  the 
simple  illustrations  of  gravitation,  a  few  words 
should  be  added  at  this  point  in  regard  to  the 
moon's  motion.  It  is  perfectly  obvious,  as  New- 
ton of  course  recognized,  that  the  calculation 


GRAVITATION  105 

of  the  moon's  motion  is  by  no  means  a  simple 
matter  unless  assumptions  are  made  which 
correspond  only  approximately  with  fact.  Thus, 
the  orbit  of  the  moon's  motion  is  not  circular, 
nor  does  the  plane  of  this  orbit  keep  a  fixed 
position  with  reference  to  the  earth ;  the  earth 
is  not  a  sphere,  nor  is  it  homogeneous ;  nor 
does  it  keep  its  shape  fixed  (owing  to  the  mo- 
tion of  the  tides).  Owing  to  these  and  other 
reasons  it  is  a  matter  of  extraordinary  diffi- 
culty to  make  exact  calculations  of  the  moon's 
motion.  Newton  himself  introduced  certain 
corrections  into  the  simple  theory ;  so  did  La- 
place and  many  later  astronomers ;  but  it  has 
only  been  within  the  past  decade  that,  owing  to 
the  great  skill  and  industry  of  Professor 
E.  W.  Brown,  now  of  Yale  University,  we 
have  had  satisfactory  means  of  calculation  of 
this  motion,  and  the  result  is  what  must  be 
called  perfect  agreement  with  observation. 
It  must  be  emphasized,  moreover,  that  in  none 
of  this  most  extensive  and  exhaustive  work 
has  it  been  found  necessary  to  modify  in  the 
slightest  Newton's  original  hypothesis.  (It  is 


106        THE  CONSTITUTION  OF  MATTER 

only  fair  to  add  that  Professor  Newcomb,  in 
a  recalculation  of  all  known  facts  referring  to 
planetary  motions,  found  that  an  extremely 
slight  modification  of  the  law,  so  far  as  dis- 
tance was  concerned,  made  certain  facts  agree 
better  with  the  theory.  This  change,  however, 
is  not  compatible  with  the  motion  of  the  moon, 
as  Professor  Brown  has  shown.  Consequently 
some  other  explanation  of  the  slight  diver- 
gence between  theory  and  observation  in  the 
motion  of  Mercury  must  be  found.) 

Now  to  return  to  the  law  of  falling  bodies, 
that  is,  to  the  question  of  weight.  The  con- 
nection between  weight  and  the  phenomenon 
of  falling  is  of  course  obvious.  The  early  phi- 
losophers, such  as  Aristotle,  asserted  as  a  self- 
evident  proposition  that  the  heavier  a  body 
was  the  faster  must  it  fall.  It  is  doubtful  if  to 
their  minds  or  to  those  of  their  followers  there 
was  anything  to  be  gained  by  trying  the  ex- 
periment. To  them,  all  questions,  whether  re- 
ferring to  nature  or  not,  were  matters  for 
intellectual  discussion  only.  The  idea  of  de- 
vising experiments  by  which  to  test  hypoth- 


GRAVITATION  107 

eses  concerning  natural  phenomena  we  owe  in 
the  main  to  Galileo.  One  of  the  first  questions 
considered  by  him  was  that  of  falling  bodies. 
He  convinced  himself  by  experiments  and  by 
simple  reasoning  that  all  bodies,  no  matter 
what  their  weight,  should  fall  towards  the 
earth  at  the  same  rate  —  excepting,  of  course, 
any  differences  introduced  by  the  presence  of 
the  air,  which  might  be  marked  if  one  body 
was  large  and  light  and  the  other  small  and 
heavy.  As  you  may  know,  Galileo's  thoughts 
on  mechanics  and  his  experiments  performed 
upon  falling  bodies,  projectiles,  etc.,  were  pub- 
lished in  a  series  of  "  Discorsi,"  which  were 
apparently  conversations  upon  philosophical 
subjects  between  three  friends.  Of  course 
there  is  never  any  difficulty  in  knowing  which 
of  these  is  voicing  Galileo's  own  thoughts. 
His  argument  in  regard  to  falling  bodies  is  as 
follows :  "  If  we  have  two  bodies  whose  natu- 
ral velocities  (according  to  Aristotle's  teach- 
ing) are  different,  it  is  clear  that,  if  we  join 
the  two,  the  faster  one  must  be  retarded  by 
the  slower,  and  the  slower  accelerated  by  the 


108        THE  CONSTITUTION  OF  MATTER 

faster.  Therefore,  if  it  were  true  that  a  large 
stone  fell  with  a  velocity  which  we  may  call  8, 
and  a  small  stone  with  a  velocity  4,  it  would 
follow  that,  if  the  two  were  joined,  the  velocity 
would  be  less  than  8.  But  the  two  together 
form  a  stone  larger  than  the  one  which,  fall- 
ing by  itself,  had  a  velocity  8 ;  and  therefore 
the  larger  stone  falls  more  slowly  than  the 
smaller,  which  is  contrary  to  the  hypothesis." 
The  conclusion,  then,  is  that  the  two  stones, 
large  and  small,  must  fall  with  the  same  veloc- 
ity. Galileo  discussed  also  the  effect  of  the 
presence  of  the  air  upon  falling  bodies,  and 
says  :  "I  believe  that,  if  the  resistance  of  the 
air  were  entirely  removed,  all  bodies  would 
fall  with  absolutely  the  same  velocity."  He 
also  performed  many  experiments  upon  falling 
bodies ;  and  it  is  perfectly  clear  that  the  logi- 
cal argument  concerning  the  subject,  which  I 
have  quoted  above,  was  not  offered  to  convince 
himself  of  the  equality  of  velocity  of  fall  for 
all  bodies ;  his  observations  had  done  that. 
Among  his  experiments  he  mentions  allow- 
ing bodies  of  different  weights  to  fall  directly 


GRAVITATION  109 

and  also  down  inclined  planes,  which  have  the 
result  of  making  the  effective  force  of  gravity 
less,  but  do  not  introduce  any  other  quality 
(except  friction,  which  can  be  ma.de  very  small). 
The  most  interesting  of  his  experiments  con- 
sisted in  comparing  the  periods  of  oscillation 
of  two  pendulums  consisting  of  fine  threads  of 
the  same  length,  one  carrying  a  cork  sphere, 
the  other  a  lead  one.  He  noted  that  during  a 
large  number  of  swings  —  until  in  fact  the 
motion  finally  died  out  —  the  periods  were  the 
same.  He  explained  the  fact  that  the  vibra- 
tions of  the  cork  pendulum  die  down  more 
rapidly  than  those  of  the  lead  one  as  due  to 
the  comparative  lightness  of  the  cork  and 
therefore  the  greater  effect  of  the  air  upon  it ; 
but  if  the  cork  pendulum  is  given  at  the  start 
a  somewhat  greater  swing  than  the  lead  one, 
there  will  come  a  time  when  the  amplitudes  of 
the  swings  of  the  two  pendulums  are  the  same, 
and,  since  their  periods  are  the  same,  they  will 
then  fall  in  the  same  time  through  paths  which 
are  identically  the  same. 

One  of  his  most  famous  experiments  was 


110        THE   CONSTITUTION  OF  MATTER 

designed  to  call  the  attention  of  a  large  audi- 
ence to  the  truth  concerning  falling  bodies. 
He  was  living  in  Pisa  at  the  time,  and  he  had 
an  assistant  carry  two  cannon  balls  of  differ- 
ent weight  to  the  highest  gallery  of  the  famous 
Leaning  Tower,  while  he  remained  at  the  bot- 
tom surrounded  by  a  numerous  company.  At 
a  given  signal  the  assistant  pushed  the  two 
balls  off  the  ledge  at  the  same  instant ;  and 
those  standing  below  saw  them  fall  side  by 
side  and  heard  them  strike  the  stone  pavement 
as  if  with  a  single  impact.  We  might  suppose 
that  every  one  who  saw  the  falling  balls  and 
heard  the  simultaneous  thud  upon  the  ground 
would  be  convinced  of  the  error  of  Aristotle's 
statement  in  regard  to  falling  bodies;  but 
quite  the  contrary  was  true.  The  spectators 
interpreted  the  observed  fact  by  believing — 
what  was  a  most  obvious  possibility  to  them  — 
that  the  laws  of  nature  had  been  perverted 
that  day,  and  they  attributed  to  Galileo  the 
power  of  a  magician,  not  of  a  philosopher.  He 
himself,  however,  believed ;  and  being  con- 
vinced that  all  bodies,  regardless  of  their 


GRAVITATION  111 

weight,  fall  alike,  he  determined  to  discover 
the  law  of  motion  of  a  falling  body. 

The  most  incidental  observation  proves  that, 
as  a  body  falls,  it  goes  faster  and  faster,  that 
is,  the  distance  traversed  is  not  proportional  to 
the  duration  of  time  of  fall;  the  velocity  of 
fall,  therefore,  increases  as  time  goes  on  and 
as  the  distance  increases.  In  attempting  to- 
express  the  facts  in  some  simple  mathematical 
form,  there  are  two  simple  hypotheses  which 
we  might  make  and  which  we  could  then  test 
by  comparing  their  deductions  with  observa- 
tion. (It  might  be,  of  course,  that  neither 
hypothesis  was  satisfactory.)  One  is  that  the 
velocity  increases  uniformly  with  the  distance 
of  the  fall;  i.e.,  that,  if  the  velocity  at  the 
end  of  a  fall  of  one  foot  is  a,  at  the  end  of 
two  feet,  it  is  %a9  etc.  Another  is  that  the 
velocity  increases  uniformly  with  the  time; 
that  is,  the  velocity  at  the  end  of  the  second 
second  is  twice  what  it  was  at  the  end  of  the 
first,  etc.  Galileo  discussed  these  two  hy- 
potheses and  dismissed  the  first  as  leading  to 
conclusions  which  were  inconceivable.  He, 


112        THE   CONSTITUTION  OF  MATTER 

therefore,  concentrated  his  attention  upon  the 
second.  He  saw  that  it  was  impossible  to  test 
this  hypothesis  directly,  because  of  the  diffi- 
culty of  measuring  the  velocity  of  a  falling 
body  at  any  instant  of  its  fall ;  and,  therefore, 
he  resorted  to  what  may  be  called  indirect 
methods.  He  showed  by  mathematical  reason- 
ing that,  if  we  assume  as  true  the  hypothesis 
that  the  velocity  increases  uniformly  with  the 
time,  the  distance  traversed  by  the  falling  body 
must  vary  as  the  square  of  the  time,  i.e.,  if 
the  distance  passed  over  in  the  first  second  is 
x,  that  passed  over  at  the  end  of  two  seconds 
is  cc2,  etc.  Owing  to  the  fact  that  a  body  fall- 
ing vertically  moves  so  very  rapidly  after  the 
first  few  seconds  that  it  would  be  with  great 
difficulty  that  one  could  determine  its  exact 
position  at  any  one  instant,  Galileo  devised  the 
most  ingenious  plan  of  having  the  body  fall 
down  an  inclined  plane  instead  of  vertically. 
This  modification  simply  dilutes  gravity,  as  it 
were,  making  the  force  less  in  a  definite  ratio, 
depending  upon  the  inclination  which  the 
plane  makes  with  the  vertical.  With  our  mod- 


GRAVITATION  113 

ern  methods  of  measuring  time,  it  would  be 
easy,  indeed,  to  carry  out  this  experiment  of 
Galileo's ;  but  he  had  at  his  disposal  no  watch, 
no  clock ;  indeed,  no  timekeeping  mechanism. 
He,  therefore,  was  forced  to  use  some  other 
method  of  determining  his  time-intervals. 
What  he  actually  did  was  to  insert  a  fine  tube 
into  a  small  opening  made  in  the  bottom  of  a 
pail;  this  he  filled  with  water,  and  he  then  ar- 
ranged to  open  and  close  the  tube  and  to  catch 
the  escaped  water.  This  water  he  weighed 
on  a  balance ;  and  he  assumed  that  the  quantity 
of  water  escaping  was  directly  proportional  to 
the  time  of  opening,  which  is  fairly  true,  so 
long  as  the  level  of  the  water  in  the  large  ves- 
sel does  not  change  greatly.  For  his  inclined 
plane  he  used  a  long  wooden  board  along  whose 
edge  he  made  a  straight  smooth  trough;  and 
for  his  falling  body  he  used  a  brass  ball,  accu- 
rately round  and  smoothly  polished.  Then, 
when  he  started  the  ball  down  the  board  he 
opened  the  tube  leading  into  the  pail  of  water, 
and  allowed  the  water  to  escape  until  the  ball 
passed  some  definite  point  on  the  board.  He 


114        THE  CONSTITUTION  OF  MATTER 

in  this  manner  compared  the  times  of  fall  for 
the  entire  length  of  the  board;  one  half  of  it, 
etc.  (He  also  in  other  experiments  set  the 
board  at  different  inclinations  to  the  vertical.) 
The  result  deduced  from  all  his  observations 
was  that  the  distance  traversed  by  a  falling 
body  varies  directly  as  the  square  of  the  time 
of  fall;  and  that  therefore  the  hypothesis  that 
the  velocity  of  a  falling  body  increases  uni- 
formly with  the  time  is  verified.  We  call  the 
time-rate  of  increase  of  velocity  by  the  word 
"acceleration";  so  the  conclusion  of  all  of 
Galileo's  experiments  is  that  the  acceleration 
of  a  body  falling  vertically  under  the  influence 
of  gravity  is  a  constant,  the  same  for  all 
bodies. 

We  may  express  this  fact  in  the  language 
of  Newton  by  introducing  his  idea  of  mass. 
When  a  body  of  mass  m  receives  under  any 
circumstances  an  acceleration  a,  we  say  there 
is  a  force  acting  upon  the  body  numerically 
equal  to  the  product  ma.  So,  if  we  call  the 
acceleration  of  a  body  falling  vertically  by 
the  symbol  g,  the  force  acting  on  it  owing  to 


GRAVITATION  115 

the  presence  of  the  earth  equals  the  product 
mg.  This,  then,  is  the  weight  of  that  body. 

Now,  in  accordance  with  Newton's  hypothe- 
sis concerning  the  interaction  of  two  bodies, 
the  force  acting  upon  any  body  near  the 
earth's  surface  is  proportional  to  the  product 
of  the  mass  of  the  body  by  that  of  the  earth 
divided  by  the  square  of  the  distance  of  the 
body  from  the  center  of  the  earth.  Owing  to 
the  enormous  disparity  between  the  radius  of 
the  earth  and  the  size  of  a  falling  body  and 
any  height  through  which  we  ordinarily  can 
let  bodies  fall,  it  is  apparent  that  we  may  con- 
sider the  distance  from  the  center  of  the  earth 
to  all  points  of  the  body  itself  as  being  the 
same  and  as  remaining  unchanged  during  the 
motion.  Therefore,  Newton's  law  of  gravita- 
tion says  that  the  force  acting  on  a  falling 
body  equals  its  mass  multiplied  by  a  quantity 
which  is  constant  and  the  same  for  bodies  of 
all  sizes  and  materials.  This  is  exactly  what 
Galileo's  experiments  indicated ;  but,  realizing 
the  importance  of  the  matter  from  the  stand- 
point of  the  verification  of  his  own  hypothesis, 


116         THE  CONSTITUTION  OF  MATTER 

Newton  determined  to  investigate  the  ques- 
tion anew.  For  this  purpose  he  made  use  of 
pendulums  which  consisted  of  long  threads 
supporting  bobs  of  different  materials.  The 
law  of  vibration  of  a  pendulum  was  known 
to  Galileo,  at  least  that  part  which  states  that 
the  square  of  the  period  of  oscillation  varies 
as  the  length ;  i.e.,  if  we  double  the  length, 
the  period  becomes  four  times  what  it  was; 
and  he  also  made  use,  as  we  saw,  of  pendulums 
for  the  purpose  of  studying  the  laws  of  falling 
bodies.  To  Galileo  the  problem  of  a  pendulum 
was  what  we  may  call  a  "kinematic"  one, 
dealing  with  the  motion  of  a  body  in  a  ver- 
tical circle,  under  a  constant  acceleration 
downwards ;  to  Newton  it  was  very  different. 
Newton  introduced  into  philosophy  the  ideas 
of  quantity  of  matter  or  mass  and  of  force ;  a 
pendulum,  then,  consists  of  a  bob  which  is 
constrained  to  move  in  a  vertical  circle  and 
which  has  a  definite  mass ;  and  under  the  force 
which  we  call  its  "  weight,"  this  bob  has  a  cer- 
tain periodic  motion.  Naturally  the  period  of 
the  motion  will  depend  upon  how  the  bob  re- 


GRAVITATION  117 

acts  under  the  influence  of  the  force;  i.e., 
upon  the  opposition  it  offers  to  this  force. 
Consequently  we  would  conclude  that  the  pe- 
riod of  oscillation  of  a  pendulum  should  in 
some  way  measure  the  ratio  of  the  weight  of 
a  body  to  its  mass.  The  exact  formula  was 
deduced  by  Newton,  and  is  one  of  the  most 
familiar  in  physics.  It  may  suffice  to  say  here 
that  the  formula  proves  that,  if  this  ratio  of 
weight  to  mass  is  constant ;  i.e.,  if  the  acceler- 
ation of  a  falling  body  is  constant,  then  the 
period  of  oscillation  of  any  one  pendulum  is 
the  same  for  any  amplitude  of  vibration  so 
long  as  it  is  small  compared  with  the  length 
of  the  pendulum  thread,  and  the  square  of  the 
period  of  oscillation  is  proportional  to  the 
length  of  the  pendulum.  Newton  accepted  as 
proved  by  numerous  observations  that  this 
formula  was  completely  verified  for  any  one 
pendulum ;  but  he  thought  that  the  question 
of  the  identity  of  the  ratio  of  weight  to  mass 
for  all  bodies  required  further  investigation. 
The  question,  expressed  differently,  is  this :  If 
two  bodies  have  the  same  weight,  as  tested  by 


118         THE  CONSTITUTION  OF  MATTER 

a  balance,  do  they  also  have  the  same  mass, 
as  tested  by  an  impact  experiment  ?  or  is  it 
possible  that  different  kinds  of  matter  are  af- 
fected differently  by  gravity,  is  there  a  spe- 
cific quality  in  gravitation  ? 

Newton,  in  order  to  dispose  of  this  question, 
constructed  two  pendulums,  each  consisting  of 
a  thread  eleven  feet  long  and  carrying  a  spher- 
ical box,  in  which  could  be  placed  different 
substances.1  He  made  these  last  all  having  the 
same  weight ;  and  since  they  were  inclosed  in 
boxes  of  the  same  size  and  shape,  the  influence 
of  the  air  upon  the  motion  of  the  two  pendu- 
lums was  the  same.  He  made  use  of  the  follow- 
ing substances :  gold,  silver,  lead,  glass,  sand, 
common  salt,  wood,  water,  and  wheat.  His 
method  was  to  allow  the  two  pendulums  to 
swing  side  by  side,  noting  the  agreement  of 
their  periods.  If  the  acceleration  is  the  same 
for  the  two  bodies,  the  two  pendulums  ought 
to  continue  to  swing  together  indefinitely. 
This  Newton  observed  to  take  place  ;  and  he 
therefore  concluded  that  the  ratio  of  the  weight 

1  Principia,  book  in,  proposition  vi. 


GRAVITATION  119 

and  mass  of  all  bodies  is  the  same.  Conse- 
quently this  feature  of  his  hypothesis  concern- 
ing gravitation  could  be  considered  verified. 

Newton  estimated  that  the  accuracy  of  his 
method  of  experimenting  was  such  that  any 
variation  in  the  agreement  of  this  gravity  ac- 
celeration for  different  bodies  greater  than  one 
part  in  one  thousand  would  have  been  observed. 
We  now  know,  however,  that  the  agreement 
is  much  better  than  this.  Bessel,  the  German 
astronomer,  made  a  large  number  of  pendulum 
observations,1  using  pendulums  of  different 
materials,  and  drew  the  conclusion  from  his 
observations  that  any  difference  which  might 
exist  was  too  minute  to  be  observed  by  his 
method,  which  allowed  a  possible  error  of  1 
part  in  60,000. 

We  may  say,  then,  that  Newton's  hypothe- 
sis has  been  verified  so  far  as  it  states  that 
gravitation  is  independent  of  the  kind  of  mat- 
ter constituting  the  attracting  bodies,  and  so 
far  as  the  law  of  distance  is  concerned,  pro- 
vided this  distance  is  of  an  astronomical  mag- 

1  Mem.  Berlin  Akad.  (1830). 


120         THE  CONSTITUTION  OF  MATTER 

nitude.  Two  questions,  however,  arise :  first, 
Does  the  law  hold  for  radio-active  bodies? 
second,  Does  it  hold  for  small  bodies  at  small 
distances  apart  ? 

Let  us  consider  the  latter  question  first. 
When  one  holds  in  his  hand  any  ordinary  body, 
say  a  pound  weight,  and  realizes  that  the  sen- 
sation of  its  weight  which  he  experiences  is 
that  due  to  the  action  of  the  whole  huge  earth, 
he  can  easily  believe  that  the  force  between 
two  bodies,  both  of  ordinary  size,  must  be  ex- 
traordinarily minute.  This,  indeed,  is  the  case ; 
and  the  utmost  refinements  of  scientific 
measurement  must  be  applied  in  order  to  make 
any  accurate  statement  with  reference  to  the 
force  of  gravitation  between  two  bodies  even 
of  moderate  dimensions.  This  has,  however, 
been  done ;  and  various  investigators,  notably 
A.  S.  MacKenzie,1  have  studied  the  accuracy 
of  Newton's  law  for  small  bodies.  This  obser- 
ver has  shown  that  for  lead  balls,  5  centi- 
meters in  diameter  and  for  distances  as  small 
as  3  centimeters,  the  law  holds  within  the  lim- 

1  Phys.  Rev.  (1894). 


GRAVITATION  121 

its  of  experimental  error.  As  to  whether  it 
holds  for  molecules,  or  for  even  small  groups 
of  molecules,  no  one  can  say.  Lord  Kelvin  has 
shown  that  a  law  of  the  kind  of  Newton's,  if 
it  does  hold  for  molecules,  might  account  for 
the  ordinary  forces  of  cohesion  in  solids ;  but 
great  difficulties  would  arise  in  applying  the 
law  to  the  molecules  of  a  gas.  As  a  matter  of 
fact,  whatever  theory  we  have  as  to  the  ulti- 
mate cause  of  gravitational  attraction,  there 
are  good  reasons  for  there  being  a  modifica- 
tion in  the  Newtonian  law  when  we  consider 
extremely  small  •  quantities  of  matter  placed 
close  together. 

The  second  question  raised  in  regard  to 
gravitation  was  one  concerning  radio-active 
matter.  Assuming  that  the  gravity-acceler- 
ation of  such  a  body  is  a  constant,  is  this  the 
same  constant  as  for  an  ordinary  piece  of  mat- 
ter? This  constant  is  the  value  of  the  weight 
of  a  body  divided  by  that  of  its  mass ;  and  it 
is  best  determined  by  using  the  body  as  the 
bob  of  a  pendulum,  and  measuring  the  period 
of  oscillation  for  a  thread  of  known  length. 


122         THE  CONSTITUTION  OF  MATTER 

Suppose  we  were  to  make  two  pendulums,  one 
having  for  its  bob  a  definite  weight  of  some 
radio-active  matter,  such  as  a  uranium  ore,  the 
other  having  for  its  bob  an  exactly  equal  weight 
of  some  ordinary  substance,  such  as  lead ;  by 
means  of  each  pendulum  we  could  obtain  the 
corresponding  value  of  the  gravity-accelera- 
tion. If  both  pendulums  gave  the  same  value 
for  this,  it  would  mean  that  the  two  bobs,  which 
have  equal  weights,  also  have  equal  masses ; 
on  the  other  hand,  if  the  two  pendulums  gave 
different  values  of  the  constant,  it  would  mean 
that  the  two  bodies  of  equal  weight,  as  tested 
by  a  balance,  had  different  masses.  Believing 
part,  at  least,  of  the  mass  of  a  body  to  be  due 
to  the  potential  energy  of  the  electric  charges 
constituting  its  atoms,  it  is  evident  that,  if  this 
potential  energy  of  a  body  contributes  to  its 
mass  and  not  to  its  weight,  —  the  latter  being 
due  to  what  we  may  call  non-electric  mass,  — • 
then  two  bodies  having  the  same  mass  would 
not  have  the  same  weight  —  and  vice  versa, 
provided  one  had  more  potential  energy  than 
the  other.  This  fact  could  be  detected  by  pen- 


GRAVITATION  123 

dulum  experiments.  A  radio-active  body  con- 
tains a  large  amount  of  potential  energy  as  is 
shown  by  its  transformation  into  the  kinetic 
energy  of  the  ejected  alpha  and  beta  particles. 
If  this  potential  energy  is  in  excess  of  that 
which  is  characteristic  of  the  ordinary  group- 
ing of  corpuscle  and  positive  charge  in  ordi- 
nary matter,  we  can  easily  test  the  question  as 
to  whether  or  not  there  is  this  difference  in  the 
ratio  of  weight  to  mass.  All  that  is  necessary 
is  to  compare  the  vibrations  of  pendulums, 
one  made  of  ordinary  matter,  the  other  of 
radio-active  matter.  This  has  been  done  by  J. 
J.  Thomson  and  more  recently  by  L.  South- 
erns,1 one  of  his  students.  The  latter  used  in 
his  experiments  pendulum  bobs  made  of  ura- 
nium oxide  and  of  lead  oxide,  and  was  unable 
to  detect  the  faintest  difference  in  the  two 
cases.  His  conclusion  was  that  a  difference  in 
acceleration  greater  than  1  part  in  200,000 
cannot  exist. 

Taking  into  account  all  the  phenomena  of 
gravitation,  we  see  that  there  is  in  the  end 

1  Proc.  Roy.  Soc.t  vol.  LXXXIV,  p.  325  (1911). 


124         THE  CONSTITUTION  OF  MATTER 

but  one  fact  to  explain,  namely,  why  it  is  that 
two  pieces  of  matter,  if  free  to  move,  ap- 
proach each  other  as  stated  in  Newton's  law. 
We  have  shown  that  the  presence  in  atoms  of 
positive  and  negative  charges  accounts  for 
part  at  least  of  their  mass ;  and  we  naturally 
ask  if  it  is  not  possible  to  account  for  gravi- 
tation as  due  to  these  same  charges  in  atoms. 
The  fundamental  law  of  electrostatics  is,  as 
we  have  seen,  that  like  charges  repel  each 
other  and  unlike  charges  attract;  and  experi- 
ments have  proved  that  the  force  varies  di- 
rectly as  the  product  of  the  charges  and  in- 
versely as  the  square  of  the  distance.  So  far 
as  any  electrical  experiment  can  tell  us,  the 
force  of  attraction  between  two  unlike  charges 
is  the  same  numerically  as  the  force  of  repul- 
sion between  two  charges  having  the  same 
values  as  in  the  previous  case  but  both  being 
of  the  same  kind.  But  electrical  experiments 
admit  of  a  test  of  this  fact  only  to  a  certain 
degree  of  accuracy ;  and  it  is  easily  seen  that, 
if  the  force  of  attraction  is  slightly  greater 
than  the  corresponding  one  of  repulsion, 


GRAVITATION  125 

there  will  be  a  resultant  attraction  between 
two  bodies,  each  of  which  is  electrically  neu- 
tral.1 The  calculation  of  the  difference  be- 
tween these  two  electric  forces  required  to 
account  for  gravitation  has  been  made  by  sev- 
eral men,  making  plausible  hypotheses  as  to 
the  values  of  the  charges  in  the  atoms;  and 
all  agree  in  the  conclusion  that  the  difference 
is  so  small  that  it  could  not  be  detected  in 
any  ordinary  electrical  experiment.  We  can 
see  also  that,  if  we  imagine  two  atoms  close 
together,  the  electrical  forces  between  the  dif- 

0  ' 

ferent  constituent  charges  will  be  sufficient  to 
change  the  relative  positions  of  the  charges  in 
the  atom  ;  and  therefore  the  effective  distance 
apart  of  the  two  atoms,  the  quantity  which 
enters  into  the  Newtonian  law  of  gravitation, 
would  be  modified,  and  the  law  would  cease 
to  hold.  The  laws  of  electric  force  would  still 
apply,  but  the  various  forces  would  combine 
into  a  single  force  in  which  the  effect  of  the 
distance  would  not  enter  as  the  square  of  the 

1  See  Sutherland,  Phil  Mag.,  vol.  vm,  p.  685  (1904); 
J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.,  vol.  xv,  p.  65  (1909). 


126         THE  CONSTITUTION  OF  MATTER 

distance  between  the  two  "centers"  of  the 
atoms. 

A  difficulty  possibly  arises  in  accepting 
this  elementary  explanation  of  gravitation 
when  we  consider  the  interval  of  time  required 
for  the  production  of  a  gravitational  effect. 
All  electric  disturbances  are  propagated  with 
a  known  finite  velocity ;  while  astronomers 
claim  that  gravitational  disturbances  travel 
with  an  infinite  velocity.  H.  A.  Lorentz1  has 
shown,  however,  that  this  difficulty  is  avoided 
if  we  express  our  hypothesis  in  a  slightly  dif- 
ferent manner,  simply  assuming  that  the  elec- 
tric disturbances  produced  by  equal  positive 
and  negative  charges  are  not  exactly  the  op- 
posite of  each  other. 

It  is  thus  seen  that  in  attempting  to  explain 
gravitation  we  assume  as  our  fundamental 
entities  positive  and  negative  electric  charges, 
which  we  picture  as  distributed  through  the 
atoms  of  matter  and  which  we  assume  have 
certain  definite  characteristic  laws  of  interac- 
tion. The  only  progress  we  have  made  is  in 

1  Proc.  Amsterdam  Academy  (1900). 


GRAVITATION  127 

showing  that  the  same  mechanism  will  account 
for  mass  and  for  weight.1 

The  only  other  serious  attempt  to  offer  an 
explanation  of  gravitation  was  made  by 
Le  Sage.  He  showed  how  a  motion  of  attrac- 
tion between  two  bodies  would  result  if  there 
were  streams  of  minute  material  particles,  i.e., 
particles  endowed  with  inertia,  traversing 
space  in  all  directions  and  if  one  made  other 
incidental  hypotheses.  The  objections  to  this 
theory,  even  when  altered  to  suit  our  modern 
point  of  view,  are  numerous  and  apparently 
unsurmountable. 

In  speaking  of  the  concepts  of  weight,  mass, 
and  force,  and  in  discussing  the  history  and 
development  of  these,  it  is  not  an  easy  matter 
to  assign  the  credit  for  the  ideas.  There  can  be 
no  doubt  but  that  Newton  was  the  first  to  in- 
troduce the  definite  concept  of  mass  as  an  in- 
herent property  of  matter  whose  quantity 
could  be  measured,  and  to  define  the  word 
force  as  equal  to  the  product  of  mass  and  ac- 

1  In  this  connection  see  papers  by  Einstein  and  Abraham 
in  the  Physik.  Zeitsch.  for  1912. 


128        THE  CONSTITUTION  OF  MATTER 

celeration  ;  and  it  is  clear  that  to  him  the  word 
"  weight "  conveyed  the  idea  of  a  force.  To 
Galileo,  on  the  other  hand,  "  weight "  meant 
at  times  the  agency  operative  in  falling  bodies 
or  in  the  tension  of  a  string  to  which  a  hang- 
ing body  was  attached ;  while  at  other  times 
it  conveyed  the  idea  of  a  property  of  the  body 
itself,  the  "  specific  gravity  "  of  the  body  being 
its  weight  divided  by  its  volume.  Galileo  had 
a  perfectly  clear  idea  of  the  property  of  a 
body  to  which  we  give  the  name  "  mass  "  and 
referred  to  it  as  having  a  value  given  by  its 
weight.  He  devotes  one  of  his  "Discourses" 
to  the  subject  of  impact,  and  describes  experi- 
ments with  the  ordinary  apparatus  of  two 
spherical  bodies  suspended  by  long  threads. 
He  notes  that  the  determining  quantity  in 
impact  is  the  product  of  the  weight  by  the 
velocity;  this  he  calls  the  "momentum."  He 
says  that  every  body  which  is  subjected  to  an 
impact  offers  a  twofold  resistance  to  the  change : 
one  factor  is  "  internal,"  confined  to  the  body 
itself  and  measured  by  its  weight ;  the  other 
factor  depends  upon  the  magnitude  of  the 


GRAVITATION  129 

motion  given  the  body  —  thus  more  effort  is 
required  to  throw  a  stone  one  hundred  paces 
than  fifty.  He  analyzes  the  effect  of  such  a 
sudden  change,  and  says  that  the  momentum 
of  a  body  experiencing  an  impact  is  made  up 
of  an  infinite  number  of  parts  each  of  which 
equals  the  product  of  the  weight  by  a  factor 
depending  upon  the  motion;  such  momenta 
increase  during  the  time  of  impact  exactly  as 
the  velocity  of  a  falling  body  increases,  the 
body  passing  through  all  degrees  of  velocity 
from  zero  up  to  the  final  velocity.  In  another 
place  he  explains  how  an  agency  for  producing 
motion,  if  acting  for  a  long  time,  will  cause  a 
greater  velocity.  It  is  thus  evident  that  Gal- 
ileo had  a  perfectly  clear  idea  as  to  the  inertia 
of  matter,  the  proper  measure  of  an  impulse, 
and  the  measure  of  a  force.  What  he  did  not 
do  was  to  define  the  mass  of  a  body  as  a  defi- 
nite property  independent  of  weight;  and  so 
he  could  not  express  his  ideas  in  mathematical 
language. 


IV 

RADIATION ;   FORMATION  OF  MOLECULES  ; 
ELASTICITY 

IN  a  previous  lecture  the  subject  of  radiant 
energy  was  mentioned ;  and  the  statement  was 
made  that  this  was  energy  emitted  by  charged 
particles  making  oscillations.  The  subject  is 
so  important  that  more  detailed  attention 
should  be  given  it. 

Bodies  of  all  kinds  are  emitting  this  radiant 
energy,  as  may  be  shown  by  instruments  of 
various  types  which  are  designed  first  to  ab- 
sorb the  energy  incident  upon  them,  and  then, 
owing  to  the  addition  of  this  energy,  to  indi- 
cate the  fact  by  a  change  in  some  of  their 
physical  properties.  Thus,  some  types  of  radi- 
ant energy  will  affect  a  photographic  plate ; 
some  affect  our  eyes,  in  which  case  we  speak 
of  the  radiation  as  being  "  luminous " ;  in 
other  cases  the  temperature  of  the  instrument 
will  be  raised,  and  this  fact  may  be  detected 


RADIATION  131 

by  a  change  in  the  volume  of  some  of  its 
parts,  by  a  change  in  its  electrical  properties, 
etc.  An  ideal  instrument  is  one  which  would 
absorb  completely  all  types  of  radiant  energy 
and  give  an  indication  by  which  we  could 
measure  exactly  the  amount  of  the  energy  re* 
ceived.  With  our  modern  methods  we  can  ap- 
proximate fairly  closely  to  this  ideal  instru- 
ment. When  radiation  is  passed  through  a 
prism  or  is  analyzed  by  some  dispersive  instru- 
ment, its  energy  is  redistributed  and  spread 
out  into  what  is  called  a  "  spectrum  "  ;  and 
the  radiation  leaving  the  prism  in  any  definite 
direction  is  characterized  by  having  a  definite 
periodicity  or  wave-length.  Thus  the  incident 
radiation  is  transformed  into  trains  of  waves, 
each  train  having  a  definite  wave-length.  The 
science  of  spectroscopy  is  the  study  of  the  an- 
alysis of  the  radiation  from  different  sources. 
It  is  found  that  solids  and  liquids,  with  very 
few  exceptions,  emit  a  "  continuous  spectrum," 
i.e.,  we  find  in  the  spectrum  of  their  radiation 
waves  of  all  wave-lengths ;  whereas  gases, 
when  stimulated  so  as  to  produce  radiation^ 


132        THE  CONSTITUTION  OF  MATTER 

emit  only  isolated  trains  of  waves,  giving  what 
is  called  a  "  discontinuous  spectrum." 

The  obvious  way  in  which  one  can  explain 
these  facts  is  to  assume  that  inside  the  mole- 
cules there  are  centers  of  emission  having 
definite  periods.  Such  a  center  will  produce 
waves  of  one  definite  wave-length  so  long  as 
it  itself  is  undisturbed ;  and  consequently  in 
the  case  of  a  gas  made  up  of  molecules  all 
alike,  or  of  groups  of  such  molecules,  there 
will  be  a  radiation  of  such  definite  trains  of 
waves  in  the  intervals  of  time  between  the 
collisions  of  the  molecules.  If  we  picture  an 
individual  molecule,  it  collides  with  another 
molecule,  then  has  a  free  path,  then  collides 
again,  etc.  During  these  free  paths  each  vibra- 
ting emitting  center  is  free  to  radiate  its 
characteristic  train  of  waves.  But,  if  the  mole- 
cules are  as  close  together  and  as  intercon- 
nected as  they  are  in  liquids  and  solids,  there 
is  no  opportunity  for  this  free  emission;  and 
consequently  the  spectrum  is  continuous.  An 
analogy  from  the  field  of  sound  is  furnished 
by  a  piano  or  a  harp ;  if  any  one  string  is 


RADIATION  133 

plucked  or  struck,  aerial  waves  of  a  definite 
frequency  are  emitted ;  but,  if  the  strings  are 
all  connected  by  a  cord,  then,  when  any  one 
string  is  struck,  all  the  strings  are  set  vibra- 
ting and  so  waves  of  all  wave-lengths  are 
emitted. 

When  the  continuous  spectrum  emitted  by  a 
solid  is  examined  by  an  instrument  which  meas- 
ures the  amounts  of  energy  carried  by  the  trains 
of  waves  of  any  definite  wave-length,  certain 
extremely  interesting  facts  are  brought  to 
light.  Let  us  define  by  a  "  black  "  body  one 
which  absorbs  completely  all  radiation  that 
may  fall  on  it.  It  is  not  difficult  to  construct 
a  body  which  practically  satisfies  this  condi- 
tion; and  in  fact  a  body  coated  with  thick 
lamp  black  is  fairly  satisfactory.  The  radia- 
tion from  such  a  body  is  of  great  theoretical 
importance  and  is  the  same  for  all  black  bodies 
at  any  given  temperature.  Many  careful  in- 
vestigations l  of  its  nature  have  been  made ; 
so  that  we  now  know  to  a  high  degree  of  ac- 

1  See  article  by  Wien,  "  Theorie  der  Strahlung,"  Encyk. 
Math.  Wissensch.,  V3,  282  (1909). 


134        THE  CONSTITUTION   OF  MATTER 

curacy  the  distribution  of  the  energy  in  the 
spectrum  of  a  black  body  at  different  tempera- 
tures. By  analyzing  these  experimental  results 
we  are  able  to  state  in  a  mathematical  formula 
the  amount  of  energy  carried  by  a  train  of 
waves  of  a  definite  wave-length  in  terms  of 
this  wave-length  and  the  temperature.  The 
formula  which  shows  the  best  agreement  with 
the  facts  of  observation  is  one  given  some 
years  ago  by  Planck. 

It  is  seen,  therefore,  that  in  explaining  the 
phenomena  of  radiation  as  connected  with 
matter  we  must  account  for  several  facts :  — 

(1)  The  production  of  radiant  energy  by 

molecules. 

(2)  The  emission  of  a  discontinuous  spec- 

trum by  any  gas. 

(3)  The  emission  by  a  black  body  of  a 
spectrum  in  which  the  energy  is  distributed" 
continuously  and  according  to  a  known  law. 

It  has  been  shown  by  Larmor,  Lorentz, 
and  others  that,  whenever  the  velocity  of  a 
charged  body  is  changed,  it  serves  as  the  cen- 
ter of  an  emission  of  radiant  energy.  We  can 


RADIATION  135 

apply  this  fact  to  the  atoms  constituting  mat- 
ter. They  consist  of  positive  and  negative 
charges ;  and  the  latter  of  these,  the  corpus- 
cles, are  certainly  in  motion,  as  is  shown  by 
their  escaping  so  easily  from  the  atoms.  The 
simplest  type  of  motion  we  can  attribute  to  the 
corpuscle  is  a  uniform  motion  in  a  circle  inside 
the  atom ;  and  here,  although  the  speed  of 
the  motion  may  be  constant,  its  direction  is 
changing  continuously,  so  there  will  be  radia- 
tion as  a  consequence.  Or,  we  can  imagine  two 
or  more  atoms  forming  a  stable  group,  and  can 
picture  a  corpuscle  making  revolutions  along 
an  orbit  lying  in  the  range  of  influence  of  the 
groups ;  here  again  there  is  a  change  of  ve- 
locity, and  therefore  there  will  be  radiation. 
Again,  if  we  consider  a  system  of  atoms  and 
corpuscles  in  which  some  corpuscles  are  leaving 
atoms  and  others  are  joining  them,  we  have 
changes  in  the  velocities  of  the  corpuscles  and 
consequently  radiation.  Other  processes  may 
be  imagined;  and  there  is  no  reason  for  not 
believing  that  all  of  them  may  take  part  in  the 
radiation  from  bodies. 


136        THE  CONSTITUTION  OF  MATTER 

The  first  two  processes  would  give  rise  to 
trains  of  waves  of  definite  wave-length;  the 
last  would  not ;  and  therefore  in  the  case  of  a 
gas  we  naturally  imagine  motions  similar  to 
the  former  as  playing  the  most  prominent  part. 
Several  serious  difficulties  arise  however.  One 
comes  from  the  great  frequency  of  vibration 
which  is  observed.  Thus,  the  number  of  vibra- 
tions per  second  which  is  characteristic  of 
those  waves  which  produce  in  our  eyes  the 
sensation  of  blue  is  75  X  1013 ;  and,  if  these 
are  caused  by  the  revolution  of  a  corpuscle  in 
an  orbit,  this  enormous  figure  is  the  number 
of  complete  revolutions  which  the  corpuscle 
must  make  each  second.  (If  there  are  several 
corpuscles  in  an  atom  pursuing  the  same  orbit, 
this  figure  is  decreased;  but  it  is  still  enor- 
mous.) Again,  the  spectrum  of  every  known 
gas  consists  of  numerous  isolated  trains  of 
waves ;  and  the  vapor  of  iron  emits  at  least 
fifteen  thousand  such  separate  and  distinct 
trains.  The  spectra  of  many  gases  consist  of 
trains  of  waves  which  are  not  distributed  at 
random,  but,  on  the  contrary,  exhibit  striking 


RADIATION  137 

regularities.  When  their  wave-lengths  are 
measured  and  compared,  it  is  seen  that  the  num- 
bers are  connected  by  simple  mathematical 
formulae ;  and,  further,  when  the  spectra  of  sim- 
ilar gases  are  compared,  the  corresponding  for- 
mulae for  them  all  are  of  the  same  form.  These 
facts  were  first  developed  extensively  by  Kay- 
ser  and  Runge l  and  certainly  have  a  most  im- 
portant bearing  upon  any  molecular  theories. 

Other  difficulties  arise  when  we  consider  the 
Zeeman  effect,  to  which  brief  reference  has 
already  been  made.  When  a  source  of  radia- 
tion is  placed  in  an  intense  magnetic  field,  each 
train  of  waves  is  replaced  by  at  least  three, 
in  some  cases  many  more ;  so  that  the  possibil- 
ity of  the  corpuscle  possessing  these  distinct 
periods  —  all  of  which  coincide  where  there  is 
no  magnetic  field  —  must  be  taken  into  ac- 
count. 

If  an  atom  contains  even  a  moderately  large 
number  of  corpuscles,  the  radiation  emitted 
by  it  is  not  that  characteristic  of  the  acceler- 
ations of  the  individual  corpuscles,  because 

1  See  Kayser,  Handbuch  der  Spektroskopie. 


138         THE  CONSTITUTION  OF  MATTER 

owing  to  the  large  number  of  oscillating  parts 
there  is  an  interaction  between  them ;  and  that 
which  finally  emerges  from  the  atom  is  a  ra- 
diation characteristic  of  the  average  accelera- 
tion of  the  corpuscles.  The  same  is  true  of  the 
radiation  produced  by  a  molecule.  Therefore 
any  definite  type  of  gaseous  molecule  would 
emit  radiation  all  of  one  definite  wave-length ; 
and  in  the  case  of  a  gas  whose  spectrum  has  one 
thousand  isolated  trains  of  waves,  we  must  as- 
sume the  existence  of  this  number  of  different 
molecules.  These  differences  in  molecules  may 
be  brought  about  in  many  ways ; l  e.g.,  there 
may  be  groups  of  two,  three,  etc. ;  some  mol- 
ecules may  be  charged,  others  uncharged,  etc. 
The  type  of  radiation  which  we  must  have 
as  the  result  of  corpuscles  leaving  and  return- 
ing to  atoms  deserves  special  attention,  because 
this  process  is  certainly  going  on  in  all  solid 
bodies.  In  gases  a  state  of  dissociation  and  re- 
combination of  the  atoms  seems  to  be  essential 
for  the  production  of  the  characteristic  radia- 
tion; and  in  this  state  we  have  violent  accel- 

i  H.  A.  Wilson,  Phil.  Mag.,  vol.  xxm,  p.  660  (1912). 


RADIATION  139 

erations  of  charges.  A  definite  amount  of 
work  is  required  to  force  a  corpuscle  out  of  an 
atom;  and  when  it  falls  back  again  into  an 
atom,  it  at  first  has  an  amount  of  kinetic  en- 
ergy equal  to  this ;  but  as  it  gradually  returns 
to  its  original  condition  inside  the  atom,  this 
energy  must  be  lost  by  a  radiation  process. 
Thus,  each  such  recombination  of  corpuscle  and 
atom  will  give  rise  to  a  pulse  of  radiant  en- 
ergy ;  and  during  a  series  of  such  recombina- 
tions there  will  be  a  series  of  such  identical 
pulses  emitted,  each  carrying  equal  amounts 
of  energy.  As  Thomson  has  recently  shown,1  it 
is  possible,  by  considering  the  radiation  from 
solids  to  be  of  this  nature,  to  calculate  where 
in  the  range  of  wave-lengths  these  pulses  will 
carry  their  maximum  energy,  and  in  this  way 
to  explain  the  origin  of  Koentgen  rays.  In 
order,  however,  to  account  for  the  periodicities 
observed  with  gases,  the  accelerations  of  the 
corpuscles  must  be  analyzed  much  further. 

We  thus  see  that  there  is  no  great  difficulty 
in  picturing  the  processes  of  corpuscular  mo- 

i  Phil.  Mag.,  vol.  xxm,  p.  449  (1912). 


140        THE  CONSTITUTION  OF  MATTER 

tion  which  will  account  for  discontinuous  and 
continuous  spectra;  but,  when  the  attempt 
is  made  to  be  more  precise  as  to  this  motion, 
so  as  to  deduce  the  exact  laws  for  the  distri- 
bution of  energy  in  the  spectrum,  it  is  found 
that  little  progress  can  be  made.  Within  re- 
cent years  grave  doubts  have  arisen  as  to 
whether  we  know  the  proper  mathematical 
laws  to  apply  to  such  minute  particles  as  cor- 
puscles or  to  the  changes  in  the  aether. 

An  interesting  question  arises  in  regard  to 
the  nature  of  the  mode  of  propagation  of  the 
radiant  energy,  which  has  an  important  bear- 
ing upon  the  nature  of  the  corpuscle,  and 
therefore  upon  the  constitution  of  the  atom. 
Up  to  within  very  recent  years  every  one  has 
pictured  the  spreading  out  of  the  disturbance 
from  any  vibrating  center  as  being  the  same 
in  all  directions ;  just  as,  when  one  drops  a 
stone  into  a  pool  of  water,  a  wave  may  be 
seen  propagated  out  having  a  continuous  cir- 
cular front ;  or,  when  an  organ  pipe  is  blown, 
one  may  hear  it  from  any  direction,  and  the 
time  required  for  the  aerial  wave  to  reach  the 


RADIATION  141 

ear  does  not  depend  upon  the  direction.  So 
we  have  supposed  it  must  necessarily  be  in  the 
case  of  light,  and  so  it  is,  as  far  as  our  eyes 
or  any  instrument  can  detect.  If  there  is  a 
flame  or  any  source  of  light,  we  can  see  it 
from  all  directions  equally  well.  But  quite  re- 
cently Thomson  has  called  attention  to  certain 
difficulties  in  the  obvious  interpretation  of  this 
fact,  which  is,  of  course,  that  there  is  a  con- 
tinuous wave-front  to  the  radiant  energy.  One 
of  these  difficulties  arises  when  we  consider 
the  phenomenon  of  ionization  of  a  gas  by 
Koentgen  rays  or  by  light.  It  has  been  proved 
that  when  radiation  of  short  wave-length  passes 
through  a  gas,  some  of  the  molecules  are  so 
disturbed  that  corpuscles  are  ejected.  The 
number  of  molecules  so  ionized  may  be  deter- 
mined ;  and  when  the  various  facts  are  studied, 
it  appears  clearly  that  the  ionization  is  much 
less  than  one  would  expect  if  the  radiation  had 
a  continuous  wave-front,  i.e.,  if  it  had  the  same 
properties  at  all  points  over  a  given  surface.1 

1  C.  T.  R.  Wilson  has  shown  (Proc.  Roy.  Soc.,  vol.  LXXXV, 
p.  285  (1911)  ;  vol.  LXXXVII,  p.  277  (1912))  this  emission  of 


142        THE   CONSTITUTION  OF  MATTER 

These  facts  and  several  others  led  Thomson 
to  make  the  hypothesis  that  all  radiant  energy 
advances  along  lines  or  rays,  which  do  not  fill 
all  the  space  through  which  the  radiation  is 
passing.  Thus,  if  the  energy  is  emitted  from 
a  point  source,  he  imagines  it  being  transmit- 
ted along  lines  drawn  radially  from  this  point. 
The  radiation  is  thought  to  proceed  from  the 
corpuscles  in  the  molecules,  and  to  consist  in 
transverse  disturbances  passing  out  along  the 
tubes  of  force  which  form  a  permanent  attach- 
ment to  the  corpuscles.  As  has  been  said  be- 
fore, Thomson  pictures  a  tube  of  force  as  hav- 
ing the  figure  of  a  rod,  and  assigns  a  small 

corpuscles  by  a  most  beautif  nl  experiment,  which  merits  de- 
scription. He  showed  many  years  ago  that,  if  there  are  mi- 
nute charged  particles  in  a  damp  atmosphere,  the  water  vapor 
will  condense  on  these  as  nuclei ;  and  it  has  been  known  since 
Roentgen's  original  investigations  on  the  radiation  that  bears 
his  name  that  these  rays  ionize  a  gas,  causing  molecules  to 
eject  corpuscles ;  these  in  turn  acting  on  other  molecules  also 
ionize  them.  In  this  last  experiment  by  Wilson  he  filled  a 
vessel  with  moist  air,  caused  it  to  expand  and  thus  become 
chilled  so  as  to  induce  condensation  of  the  water  vapor,  then 
within  one  twentieth  of  a  second  he  allowed  Roentgen  radi- 
ation to  enter  the  vessel.  There  was  evidence  of  the  forma- 
ation  of  minute  drops  along  definite  straight  lines  ;  and  pho- 
tographs were  taken  showing  the  trains  of  drops. 


RADIATION  143 

number  of  them  to  each  corpuscle.  He  attrib- 
utes to  them  a  real  existence,  and  has  shown 
how  the  mass  of  the  corpuscles  may  be  explained 
if  we  assign  a  certain  amount  of  bound  aether 
to  each  tube. 

In  order  to  have  the  wave-like  disturbances 
pass  along  them  we  must  assign  them  a  defi- 
nite elasticity ;  and  in  order  for  these  waves  to 
have  the  velocity  characteristic  of  light,  there 
must  of  course  be  a  definite  relation  between 
the  density  of  the  bound  aether  and  this  elas- 
ticity. The  passage  of  the  energy  along  these 
tubes  would  not  be  unlike  the  passage  of  a 
transverse  pulse  along  a  tightly  stretched 
string.  Then,  if  we  wish  to  picture,  on  this 
theory,  the  outward  advance  of  a  wave  from  a 
point  source,  we  think  of  a  spherical  surface 
expanding  outward,  but  active,  so  far  as  light, 
ionization,  etc.,  are  concerned,  only  at  certain 
isolated  points. 

Faraday  himself  had  this  same  view,  for  in 
one  of  his  papers  he  said :  "  The  view  which 
I  am  so  bold  to  put  forward  considers  there- 
fore radiations  as  a  high  species  of  vibration 


144        THE  CONSTITUTION  OF  MATTER 

in  the  lines  of  force  which  are  known  to  con- 
nect particles  and  also  masses  together." 
Thomson  quotes  this  in  his  book  "Electricity 
and  Matter,"  and  adds :  "  The  Faraday  tubes 
stretching  through  the  aBther  cannot  be  re- 
garded as  entirely  filling  it.  They  are  rather 
to  be  looked  upon  as  discrete  threads  embedded 
in  a  continuous  aether,  giving  to  the  latter  a 
fibrous  structure ;  but  if  this  is  the  case,  then 
on  the  view  we  have  taken  of  a  wave  of 
light  the  wave  itself  must  have  a  structure; 
and  the  front  of  the  wave,  instead  of  being, 
as  it  were,  uniformly  illuminated,  will  be  rep- 
resented by  a  series  of  bright  specks  on  a  dark 
ground,  the  bright  specks  corresponding  to  the 
places  where  the  Faraday  tubes  cut  the  wave 
front."  It  is  only  fair  to  add  that  Thomson's 
theory  has  found  few  supporters ;  and  other 
explanations  of  the  smallness  of  the  ionization 
of  gases  by  Roentgen  rays  may  be  given. 

The  mechanism  of  emission  of  radiation  by 
molecules  is  not  as  difficult  to  imagine  as  are 
certain  features  of  its  absorption1  by  mole- 

1  See  Schuster,  Theory  of  Optics,  2d  edition,  chap.  xi. 


ABSORPTION  145 

cules.  As  has  been  said,  when  radiant  energy 
is  absorbed  by  a  body,  the  energy  may  be  con- 
sumed in  producing  various  effects;  among 
these  we  may  name  vision,  photographic  ac- 
tion, fluorescence,  etc. ;  but  in  the  great  ma- 
jority of  cases  the  final  result  of  the  absorption 
is  rise  in  temperature.  There  can  be  no  doubt 
but  that  this  condition  is  due  to  an  increased 
kinetic  energy  on  the  average  for  all  the  mole- 
cules of  the  absorbing  body,  where  emphasis 
is  laid  upon  the  word  molecules.  Now  the  im- 
mediate absorption  process  must  be  one  con- 
cerned with  corpuscles;  the  corpuscles  of  an 
atom  cause  the  radiation,  those  of  another  must 
absorb  it.  There  can  be  no  doubt  but  that  this 
absorption  process  must  be  dependent  upon  res- 
onance. The  fact  that  a  corpuscular  system  can 
and  does  under  certain  conditions  emit  radia- 
tion of  a  definite  periodicity  proves  that,  if  this 
radiation  were  to  fall  upon  another  system 
capable  of  emitting  radiation  of  the  same  peri- 
odicity, this  latter  system  will  absorb  a  portion 
of  the  incident  radiation.  (Just  as,  if  we  have 
two  tuning-forks  which  have  the  same  fre- 


146        THE  CONSTITUTION  OF  MATTER 

quency,  and,  if  one  of  the  forks  is  set  vibrat- 
ing, the  aerial  waves  emitted  by  it  will  fall  upon 
the  second  fork  and  being  absorbed  by  the  lat- 
ter will  set  it  in  vibration.)  If  radiation  having 
any  definite  periodicity  falls  upon  any  cor- 
puscle, a  certain  amount  of  energy  will  be 
absorbed  by  the  latter,  regardless  of  its  own 
condition  or  its  own  periodicity;  but  the  amount 
varies  greatly.  In  any  case,  however,  the  be- 
ginning of  the  process  of  absorption  must  be 
this  increase  in  kinetic  energy  of  the  cor- 
puscles of  the  absorbing  molecules.  The  ques- 
tion then  arises  as  to  how  this  energy  becomes 
distributed  among  the  molecules  themselves, 
because,  as  we  have  said,  rise  in  temperature 
requires  this.  It  must  be  shown  how,  at  the 
moment  of  collision  between  two  molecules, 
one  having  corpuscles  which  have  gained 
energy  by  absorption,  there  is  a  transformation 
of  this  energy,  so  that  the  two  molecules 
separate  with  greater  velocities  than  they 
would  have  had  if  there  were  not  this  ab- 
sorbed energy.  The  exact  process  by  which 
this  takes  place  is  not  clear ;  the  initial 


ABSORPTION  147 

and  final  facts  are,  however,  perfectly  defi- 
nite.1 

This  transformation  of  the  radiant  energy 
which  has  been  absorbed  by  corpuscular  sys- 
tems into  the  irregular  kinetic  energy  of  the 
molecules,  which  is  manifest  to  our  senses  by 
the  production  of  some  heat-effect,  such  as  rise  in 
temperature,  is  not,  of  course,  the  only  way  in 
which  such  absorbed  energy  is  spent.  There  is 
a  large  class  of  bodies  which  do  not  show  any 
marked  change  of  temperature  when  there  is 
absorption,  but  emit  an  equivalent  amount  of 
radiant  energy  themselves.  In  some  cases  this 
energy  is  emitted  only  during  the  actual  time 
of  the  absorption  of  the  incident  energy ;  such 
bodies  are  called  "  fluorescent "  :  other  bodies 
continue  to  emit  energy  for  some  time  after 
the  incident  energy  is  shut  off ;  such  are  called 
"phosphorescent."  The  facts  with  reference 
to  these  phenomena  have  been  investigated 

1  J.  H.  Jeans,  in  his  Dynamical  Theory  of  Gases  (Cam- 
bridge, 1904),  discusses  some  of  the  features  of  this  problem 
with  great  success,  and  has  shown  how  many  of  the  difficul- 
ties in  the  study  of  the  redistribution  of  the  energy  may  be 
solved. 


148        THE  CONSTITUTION  OF  MATTER 

with  great  care;  but  no  theory  to  account 
for  them  which  is  really  satisfactory  has  been 
advanced  thus  far.  For  purposes  of  helping 
our  imaginations,  it  is  found  useful  to  think  of 
a  molecule  of  a  fluorescing  or  phosphorescing 
body  as  consisting  of  two  distinct  parts,  the  func- 
tion of  one  being  to  absorb  the  radiant  energy, 
that  of  the  other,  to  emit  the  characteristic 
radiation.  These  two  parts  are  thought  of  as  so 
connected  that,  when  the  energy  of  the  first  part 
increases  to  a  certain  amount,  there  is  a  stimu- 
lation of  the  second  part ;  and,  as  a  matter  of 
fact,  there  must  be  several  modes  of  connec- 
tion between  the  two  parts.  By  far  the  most 
important  investigation  of  fluorescence  is  that 
by  Professor  R.  W.  Wood,  of  the  Johns  Hop- 
kins University,  who  had  studied  this  phenome- 
non in  sodium  vapor,  mercury,  and  other  gases. 
One  of  the  most  interesting  facts  discovered 
by  him  was  the  striking  effect  upon  the  phe- 
nomena of  the  addition  to  the  fluorescing  gas 
of  a  small  quantity  of  some  neutral  gas.  This  is 
not  the  place,  however,  to  go  into  any  detailed 
description  of  these  beautiful  experiments. 


FORMATION   OF  MOLECULES  149 

Another  most  important  property  of  matter 
is  that  referring  to  the  formation  of  molecules. 
This  is  the  field  of  the  science  of  chemistry. 
The  fundamental  physical  entities  are  the  cor- 
puscle and  the  corresponding  positive  charge ; 
or,  if  one  prefers,  the  corpuscle  and  the  neu- 
tral atom.  These  atoms  can  combine  in  definite 
groups,  which  have  an  existence  as  such ;  of 
these  there  are  two  kinds,  called  molecules 
and  ions.  We  use  the  word  molecule  to  ex- 
press a  minute  part  of  those  forms  of  matter 
which  we  can  isolate  from  other  bodies,  e.g., 
copper,  hydrogen  gas,  etc.  When  salts  or 
acids  are  placed  in  solution,  e.g.,  when  com- 
mon sulphuric  acid  is  poured  into  water,  a  cer- 
tain proportion  of  the  acid  molecules  are  broken 
up  into  smaller  parts  in  the  act  of  going  into 
solution ;  it  is  of  course  a  question  of  the  rela- 
tive potential  energy  of  these  parts  and  the 
original  molecules.  These  fragments  of  the 
molecules  of  the  salt  or  acid  are  always  electri- 
cally charged  and  are  called  ions,  for  reasons 
which  are  clear  to  any  one  familiar  with  the 
phenomena  of  electrolysis. 


150        THE  CONSTITUTION  OF  MATTER 

We  picture  these  ions  as  moving  to  and  fro 
in  the  liquid,  recombining  to  form  molecules, 
then  dissociating  again,  etc.  Both  the  mole- 
cules and  the  ions  are  in  motion  through  the 
body  of  the  liquid ;  and,  when  a  steady  state 
is  reached,  as  many  molecules  are  dissociated 
in  any  small  interval  of  time  as  are  formed  by 
recombination.  Such  a  state  is  what  we  call 
"  statistical  equilibrium."  When  an  ion  is 
formed  by  the  resolution  of  a  molecule,  it 
does  not  remain  distinct,  but  collects  around 
itself  a  number  of  the  neutral  molecules  of 
the  liquid;  so  that  the  actual  moving  part  is 
a  relatively  large  body,  made  up  mostly  of 
neutral  molecules,  but  controlled  electrically 
by  the  charged  fragment  of  a  dissociated 
molecule.  These  ions  cannot  be  removed  as 
such  from  the  liquid  through  which  they  are 
moving,  and  therefore  are  not  molecules. 
(We  can  also,  as  has  been  said  repeatedly, 
ionize  a  gas,  i.e.,  make  it  an  electric  con- 
ductor; but  in  this  case  the  ions  are  a  corpus- 
cle and  the  positive  charged  remnant  of  a 
molecule,  each  with  an  atmosphere  of  the 


MOLECULES  151 

gaseous  molecules  attached  unless  the  gas  is 
greatly  rarified.) 

One  of  the  ions  formed  from  sulphuric  acid 
is  S04,  a  group  formed  of  one  atom  of  sul- 
phur and  four  of  oxygen.  This  group  cannot 
exist  as  such,  uncharged  and  taken  out  of  the 
water;  in  other  words  it  cannot  become  a 
molecule.  Another  ion  formed  from  sulphuric 
acid  is  a  charged  hydrogen  atom;  but,  in 
order  to  obtain  hydrogen  gas,  this  atom  must 
lose  its  charge  and  be  combined  with  another 
uncharged  hydrogen  atom ;  or  we  may  con- 
sider it  as  retaining  its  charge  and  combining 
with  another  hydrogen  atom  having  an  op- 
posite charge ;  for  hydrogen  gas  consists  of 
hydrogen  molecules,  each  of  which  is  electri- 
cally neutral  and  consists  of  two  hydrogen 
atoms.  The  sulphuric  acid  molecule  is  electri- 
cally neutral  and  is  a  combination  of  two  atoms 
of  hydrogen,  one  of  sulphur  and  four  of  oxy- 
gen. Similarly,  all  molecules  are  neutral  and 
consist  of  combinations  of  atoms;  and  so  any 
theory  of  the  formation  of  molecules  must 
be  based  upon  the  two  fundamental  facts : 


152        THE  CONSTITUTION  OF  MATTER 

(1)  that  however  the  individual  atoms  may  be 
charged  there  must  be  equal  amounts  of  posi- 
tive and  negative  charges ;  and  (2)  that  the 
forces  holding  the  parts  together  must  be 
those  which  produce  a  condition  of  stable 
equilibrium  under  existing  conditions  of  tem- 
perature, pressure,  and  environment. 

The  idea  that  molecules  consist  of  parts 
held  together  by  electrical  forces  is  almost  as 
old  as  the  science  of  chemistry ;  but  no  suc- 
cess was  had  in  offering  a  satisfactory  explana- 
tion of  the  diverse  facts  until  J.  J.  Thomson 
..made  his  epoch-making  suggestion  in  regard 
to  the  nature  of  an  atom.  We  shall  take  up 
presently  the  details  of  his  hypothesis;  but 
for  the  purposes  at  hand  we  can  picture  the 
atom,  as  we  have  been  doing  for  some  time, 
as  consisting  of  a  positive  charge  occupying  a 
continuous  central  nucleus  and  an  equal  nega- 
tive charge  consisting  of  discrete  corpuscles. 
We  can  think  of  the  corpuscles  as  existing 
outside  the  positive  electrification  and  con- 
nected with  it  by  tubes  of  force,  or  as  distrib- 
uted through  the  volume  occupied  by  the 


MOLECULES  153 

positive  charge.  An  important  point  to  em- 
phasize is  that  a  definite  volume  in  space  can- 
not be  thought  of  as  being  occupied  by  one 
atom  to  the  exclusion  of  another ;  because, 
an  atom  being  defined  by  its  mass,  and  mass 
at  least  in  part  being  conditioned  by  the  pres- 
ence of  potential  energy,  we  can  have  the 
potential  energy  in  any  volume  altered  by 
the  addition  of  more  energy.  If  we  picture, 
then,  two  atoms  coming  close  together,  we  can 
imagine  the  passage  of  one  corpuscle  from 
one  atom  to  the  other ;  this  would  result  in 
one  atom  becoming  negatively  charged,  the 
other  positively ;  and,  owing  to  the  force  of 
attraction  between  two  unlike  electrical 
charges,  these  two  atoms  might  be  held  to- 
gether and  thus  form  a  molecule.  The  funda- 
mental part  of  the  theory,  and  the  one  requir- 
ing explanation,  is  the  passage  of  the  corpuscle 
from  one  atom  to  another.  Why  should  it  not 
remain  associated  with  its  own  atom  ?  We  can 
easily  offer  an  explanation  in  terms  of  poten- 
tial energy.  It  is  a  general  statement  of  fact 
that  motions  and  changes  in  nature  take  place 


154        THE  CONSTITUTION  OF  MATTER 

of  themselves,  if  they  occur  at  all,  in  such  a 
manner  that  the  potential  energy  of  the  whole 
system  becomes  less.  Thus,  as  was  explained  in 
the  first  lecture,  a  heavy  body  falls  towards  the 
earth  if  left  to  itself,  and  the  potential  energy 
decreases ;  a  compressed  spring  or  bent  bow, 
if  released,  returns  to  its  "  natural "  condition, 
the  potential  energy  of  the  strain  vanishing, 
etc.  There  is  of  course  in  each  atom  a  definite 
amount  of  potential  energy,  depending  upon 
the  number  of  corpuscles  and  their  arrange- 
ment, and  the  amount  of  such  energy  will 
vary  for  atoms  of  different  elements.  Then, 
in  accounting  for  the  formation  of  a  molecule 
made  up  of  two  different  atoms,  e.g.,  one  of 
hydrogen  and  one  of  chlorine,  which  combine 
to  form  a  molecule  of  hydrochloric  acid,  we 
might  offer  an  explanation  by  saying  that 
the  configuration  of  the  two  different  atoms' 
is  such  that  although  the  removal  of  the  cor- 
puscle from  one  atom  might  require  work, 
this  is  offset  and  more  by  the  loss  in  potential 
energy  owing  to  its  addition  to  the  other,  so 
that  on  the  whole  the  potential  energy  is  de- 


MOLECULES  155 

creased.  But  at  first  sight  this  explanation 
would  not  apply  to  two  identical  atoms,  e.g., 
two  hydrogen  atoms.  Yet  we  can  see  that 
there  is  no  reason  to  believe  that  the  change 
in  the  potential  energy  due  to  the  removal  of 
a  corpuscle  is  equal  to  that  produced  by  the 
addition  of  one  to  the  same  atom.  (If  we  add 
a  pint  of  water  to  a  pitcher  already  nearly  full, 
some  will  run  over;  while,  if  we  remove  a 
pint,  no  such  catastrophe  will  occur.)  Thus  the 
reason  for  the  formation  of  molecules  is  re- 
duced to  a  general  principle  relating  to  poten- 
tial energy  in  all  its  forms;  but  it  must  be 
remembered  that  this  is  in  the  end  little  more 
than  a  description ;  not  an  explanation. 

The  theory  given  above  assumes  that  each 
of  the  atoms  making  up  a  molecule  is  itself 
electrically  charged  ;  this  is  not  essential.  All 
that  it  is  necessary  to  assume  is :  (1)  that  there 
are  electric  forces  between  two  or  more  atoms ; 
and  (2)  that  the  potential  energy  of  the  sys- 
tem is  decreased  by  the  atoms  arranging  them- 
selves in  definite  groups.  For  example,  each 
atom  in  a  molecule  may  act  like  an  electric 


156        THE  CONSTITUTION   OF  MATTER 

doublet,  consisting  of  two  equal  positive  and 
negative  charges  at  a  minute  distance  apart. 
Valency,  etc.,  can  be  explained  on  this  theory 
as  well  as  on  the  former. 

An  idea  which  has  played  an  important 
part  in  chemistry  and  especially  in  electro- 
chemistry is  that  of  "  valency."  Experiments 
have  shown  that  in  the  composition  of  stable 
compounds  we  may  consider  each  atom  as 
having  a  small  definite  number  of  modes  of 
attachment  to  other  atoms.  For  instance,  the 
hydrogen  atom  has  but  one,  i.e.,  if  it  is  attached 
to  any  other  atom,  it  cannot  be  attached  to  an 
additional  one  at  the  same  time;  the  chlorine 
atom  has  also  but  one ;  the  oxygen  atom  has 
two;  the  carbon  atom  has  four,  etc.  Thus 
stable  molecules  are  H2  consisting  of  two 
atoms  of  hydrogen;  H20  consisting  of  one 
atom  of  oxygen  and  two  of  hydrogen  ;  HC1, 
consisting  of  one  atom  of  hydrogen  and  one 
of  chlorine ;  CH^ ;  etc.  Expressed  in  a  differ- 
ent way,  we  may  say  that,  to  form  a  stable 
molecule  by  the  combination  of  hydrogen 
atoms  with  one  atom  of  any  element  a  definite 


MOLECULES  157 

number  of  the  former  is  required ;  this  num- 
ber is  called  the  " valency"  of  the  element 
•which  furnishes  the  single  atom.  For  experi- 
ments prove  that  in  the  formation  of  any 
stable  molecule  each  atom  retains  its  valence; 
so  that  an  atom  having  a  valency  of  two,  for 
instance,  is  combined  with  two  atoms  each 
having  a  valency  of  one,  or  with  a  single  atom 
having  a  valency  two.  Expressed  in  this  way 
we  say  that  hydrogen  has  the  valency  one ;  so 
has  chlorine ;  oxygen  has  the  valency  two ; 
carbon,  four,  etc.1 

It  is  true  that  hydrogen  and  oxygen  unite 
to  form  a  compound  containing  an  equal  num- 
ber of  atoms  of  each ;  but  it  is  not  as  stable 
as  the  molecule  of  water.  The  same  is  true 
of  many  other  atoms ;  such  compounds  are 
called  "  unsaturated."  It  is  well  known  also 
that  an  atom  may  have  a  definite  valence  as 
shown  by  a  large  number  of  compounds,  but 

1  The  "  hydroxyl  group  "  OH,  consisting  of  one  atom  of 
oxygen  and  one  of  hydrogen,  has  a  valency  one  ;  and  the 
facts  concerning  the  valency  of  any  atom  are  shown  most 
clearly  by  the  number  of  such  groups  which  combine  with 
the  atom  in  question  to  form  a  stable  molecule. 


158        THE   CONSTITUTION  OF  MATTER 

that  in  compounds  of  a  different  character  it 
may  have  quite  a  different  valence.  These 
facts  must  be  explained  by  any  theory  of  the 
constitution  of  the  atom,  if  it  is  to  be  consid- 
ered satisfactory. 

Since  we  think  of  molecules  being  formed 
by  the  grouping  of  atoms,  each  of  which  has 
lost  or  gained  corpuscles,  it  is  evident  that 
the  facts  of  valency  can  be  explained  by  say- 
ing that  any  definite  atom  can  lose  or  gain 
one,  two,  etc.,  corpuscles  and  be  stable ;  and 
that  an  element  whose  valency  is  one  is  such 
that  any  of  its  atoms  can  lose  (or  gain)  one 
corpuscle  and  be  stable,  but  would  be  unstable 
if  it  lost  (or  gained)  two ;  an  element  whose 
valency  is  two  is  one  whose  atoms  might  lose 
(or  gain)  one  corpuscle  and  be  stable,  but 
whose  stability  would  be  greater  if  they  lost 
(or  gained)  two.  We  can  learn  whether  an 
atom  in  general  loses  a  corpuscle  or  gains  one 
by  experiments  upon  the  ions  formed  in  the 
solution  of  salts  and  acids.  Thus  it  is  known 
that  a  hydrogen  atom  as  a  rule  loses  a  cor- 
puscle, while  an  oxygen  atom  gains  two.  So, 


MOLECULES  159 

in  the  molecule  of  water  vapor,  H20,  we  think 
of  a  compound  of  two  hydrogen  atoms,  each 
of  which  has  lost  a  corpuscle,  and  an  oxygen 
atom  which  has  gained  the  two.  Similarly  in 
the  molecule  of  copper  oxide,  CuO,  we  think 
of  a  copper  atom  which  has  lost  two  corpuscles 
and  an  oxygen  atom  which  has  gained  them. 
(Other  compounds  of  hydrogen  and  oxygen 
and  of  copper  and  oxygen  are  known,  as  I  have 
said,  but  they  are  not  as  stable  as  those  men- 
tioned.) Thus,  we  think  of  the  atoms  of  each 
element  having  the  possibility  of  losing  or  of 
gaining  one,  two,  or  more  corpuscles ;  but  we 
see  that  these  atoms  after  they  have  lost  or 
gained  a  definite  number  of  corpuscles  are 
more  stable  than  if  they  had  lost  or  gained 
a  different  number.  Thus,  a  hydrogen  atom, 
whose  valence  is  one,  will  be  stable  in  a 
molecule  where  it  has  lost  but  one  corpus- 
cle; an  oxygen  atom,  whose  valence  is  two, 
is  stable  if  it  has  gained  one  corpuscle,  but 
much  more  so  if  it  has  gained  two,  etc.  An 
element  whose  atoms  remain  stable  after  the 
removal  of  one  or  more  corpuscles  is  called 


160        THE  CONSTITUTION  OF  MATTER 

"  electro-positive  "  ;  while  one  whose  atoms 
remain  stable  after  the  addition  of  one  or 
more  corpuscles  is  called  "  electro-negative." 
There  are  some  elements  whose  atoms  do  not 
form  molecules  with  other  atoms,  for  instance, 
helium,  argon,  etc.  We  picture  then  these 
atoms  as  being  at  the  same  time  molecules, 
and  as  not  being  able  to  remain  charged  per- 
manently ;  i.e.,  if  one  of  them  loses  a  corpus- 
cle, it  will  by  virtue  of  its  electric  force  attract 
to  itself  another,  becoming  neutral  again. 

We  have  spoken  so  far  as  if  every  molecule 
might  be  considered  as  made  up  of  discrete 
atomic  parts,  each  part  charged,  but  the  total 
molecular  charge  being  zero.  This  would  im- 
ply that,  if  we  were  to  disrupt  a  gaseous  mole- 
cule into  its  atoms,  or  into  atomic  groups,  as 
may  be  done  by  the  impact  of  the  canal  rays 
in  a  vacuum  tube,  we  would  find  each  atom  or " 
each  group  charged  and  we  would  certainly 
expect  to  find  each  particular  kind  of  atom 
always  charged  the  same  way ;  e.g.,  a  hydrogen 
atom  always  positive,  a  chlorine  atom  always 
negative,  etc.  As  a  matter  of  fact  this  is  not 


ELASTICITY  161 

true ;  when  a  large  number  of  gaseous  mole- 
cules are  disrupted,  each  into  two  parts,  these 
seem  to  have  on  the  average  the  same  electrical 
properties.1  This  probably  means  that  each 
of  the  parts,  e.g.,  each  atom,  contains  equal 
amounts  of  positive  and  negative  electricity, 
forming  a  "doublet."  This  would  not  exert 
any  force  at  a  distance ;  but  two  such  doublets, 
if  brought  close  together  in  a  definite  way, 
would  attract  each  other,  and  thus  two  such 
parts  might  form  a  molecule.  In  order  to  form- 
ulate the  condition  for  the  formation  of  a 
molecule  with  this  point  of  view  we  may  use 
the  concept  of  potential  energy  as  we  have 
before. 

The  other  general  properties  of  matter  of 
which  we  have  not  yet  spoken  are  those  which 
refer  specially  to  the  size  and  shape  of  bodies. 
We  distinguish  between  solids,  liquids,  and 
gases ;  between  bodies  which  are  elastic,  like 
steel,  and  those  which  are  plastic,  like  putty ; 
between  fluids  which  are  viscous,  like  pitch, 
and  those  which  are  limpid,  like  water,  etc. 

1  J.  J.  Thomson,  Phil.  Mag.,  vol.  xxiv,  p.  209  (1912). 


162        THE  CONSTITUTION  OF  MATTER 

Some  of  these  properties  we  can  explain  as 
being  direct  consequences  of  the  fact  that 
molecules  have  mass.  For  instance,  if  we  have 
a  gas  enclosed  in  a  cylinder  which  is  fitted 
with  a  piston,  and  if  we  push  in  the  piston  so 
as  to  compress  the  gas  and  then  withdraw  it 
to  its  original  position,  the  gas  expands  again, 
returning  to  its  previous  volume;  so  we  say 
that  a  gas  is  perfectly  elastic.  (If  we  cannot 
see  into  the  interior  of  the  cylinder,  we  might 
think  when  we  were  pushing  in  the  piston  that 
we  were  compressing  a  spiral  coiled  spring.) 
This  property  of  a  gas  follows  at  once  from 
the  molecular  motions  in  the  gas.  The  mole- 
cules are  moving  at  random  in  all  possible  di- 
rections, impinging  on  the  piston  and  there- 
fore requiring  a  force  to  be  applied  to  it  to 
keep  it  from  being  pushed  outwards;  further, 
when  the  piston  is  withdrawn,  leaving  an  empty 
space  behind  it,  of  course  the  moving  molecules 
instantly  penetrate  it.  The  viscosity  of  a  fluid 
is  indicated  by  the  slowness  with  which  it 
flows;  it  is  due  to  a  type  of  friction.  As  the 
fluid  moves  through  a  tube  or  pipe,  the  layer 


VISCOSITY  163 

in  contact  with  the  wall  remains  practically  at 
rest;  the  next  layer  moves  slowly,  the  next 
more  rapidly,  etc. ;  the  fastest  portion  of  the 
fluid  being  that  close  to  the  axis.  Thus  we 
have  the  problem  of  considering  two  layers 
moving  in  the  same  direction,  but  with  different 
velocities.  We  all  know,  from  the  illustrations 
of  the  flowing  of  water  and  gas  in  our  houses, 
that  in  order  to  maintain  this  flow  we  must 
have  a  difference  in  pressure  at  the  two  ends 
of  the  pipe,  thus  producing  a  force  which 
makes  the  flow.  In  order  to  explain  the  phe- 
nomenon we  must  show  that  in  the  case  of 
the  two  layers  moving  with  different  velocities 
the  one  which  has  the  less  velocity  exerts  a 
backward  force  on  the  other  so  that  the  motion 
of  the  latter  would  cease  were  it  not  for  the 
pressure.  It  is  a  very  simple  matter  to  show 
that  this  retarding  force  is  an  immediate  con- 
sequence of  the  wandering  or  diffusion  of 
molecules  across  the  imaginary  surface  between 
the  two  contiguous  layers.  Others  of  these 
specific  properties  of  bodies  may  be  explained 
in  a  similar  manner;  but  the  number  of  such 


164        THE  CONSTITUTION  OF  MATTER 

is  limited.  In  the  main  we  are  driven  simply 
to  describe  the  phenomena,  introducing  per- 
haps the  word  "force,"  which  of  course  is  in 
no  sense  an  explanation.  Thus  we  think  of  a 
solid  as  made  up  of  molecules  closely  packed 
together  and  acted  on  by  such  forces  as  pre- 
vent in  general  any  individual  from  wandering 
far  away;  it  will  vibrate  about  a  definite  central 
position,  impinge  on  other  molecules,  etc.  If 
the  solid  is  deformed  very  slightly,  e.g.,  by 
compression,  bending,  twisting,  these  intra- 
molecular forces  are  so  changed  —  or  new  ones 
of  such  a  nature  arise — that,  if  the  deforming 
agency  is  removed,  the  solid  returns  to  its  orig- 
inal condition.  Solids  differ  greatly  in  regard 
to  the  magnitude  of  the  original  molecular 
forces,  and  the  consequent  chance  that  a  mole- 
cule has,  owing  to  its  velocity,  of  escaping  from 
the  surface  of  the  solid.  Thus,  if  two  soft" 
solids  such  as  gold  and  lead  are  placed  in  con- 
tact, there  is  a  progressive  diffusion  of  gold 
into  the  lead ;  the  molecules  intermingle. 
Again,  solids  differ  greatly  in  regard  to  the 
amount  of  deformation  they  can  undergo  and 


MOLECULAR  FORCES  165 

still  be  able  to  return  to  their  original  condi- 
tion ;  in  some  cases  when  this  limit  is  reached, 
the  molecules  are  moved  into  other  positions 
of  equilibrium,  e.g.,  lead,  putty;  in  others 
the  configuration  of  the  molecules  is  so  broken 
up  that  the  solid  is  permanently  weakened, 
and  the  solid  is  more  easily  fractured,  e.g., 
brass,  steel,  etc.  So  I  could  continue,  almost 
indefinitely,  describing  the  various  types  of 
solids  and  liquids ;  but  little  would  be  gained 
from  the  standpoint  of  knowledge.  No  serious 
attempt  has  been  made  to  advance  hypotheses 
sufficient  to  account  for  these  molecular  forces,1 
the  truth  being  that  with  our  fundamental 
ideas  of  the  structure  of  an  atom  and  of  a 
molecule  it  is  not  at  all  difficult  to  see,  in  a 
general  way,  how  these  forces  arise;  and  the 
differences  in  the  structure  of  different  mole- 
cules, as  shown  by  their  varied  properties, 
indicate  the  reasons  for  the  different  elastic 
forces.  When  we  say  that  experiments  prove 
that  a  molecule  is  electrically  neutral,  we  mean 
that  there  are  in  it  equal  amounts  of  positive 
1  See  Mills,  Phil.  Mag.,  vol.  xxiv,  p.  483  (1912). 


166        THE  CONSTITUTION  OF  MATTER 

and  negative  charges,  as  shown  by  their  action 
at  points  far  distant  from  the  molecule,  in 
comparison  with  the  size  of  the  molecule  itself. 
But  unless  the  centres  of  action  of  the  two 
charges  agree  exactly,  and  unless  the  two 
charges  themselves  are  exactly  equal,  this  neu- 
trality of  action  will  cease  to  exist  for  points 
as  near  to  a  molecule  as  is  another  one.  You 
can  see,  therefore,  the  elements  of  a  theory 
which  has  sufficient  flexibility  to  explain  al- 
most any  type  of  molecular  force. 

I  cannot  leave  this  subject  of  the  general 
properties  of  the  size  and  shape  of  bodies 
without  referring  to  a  most  interesting  conclu- 
sion drawn  by  Fitzgerald  and  by  Lorentz  from 
certain  observations  made  in  regard  to  bodies 
which  are  moving  rapidly  through  space.1 
Michelson  and  Morley  performed  many  years 
ago  a  series  of  experiments  with  the  object  of- 
studying  the  effect,  if  any,  upon  the  period- 
icity of  a  beam  of  light  of  altering  the  direc- 
tion of  the  beam  with  reference  to  the  motion 

1  See  Whittaker,  History  of  the  Theories  of  the  JEther, 
p.  432. 


MOLECULAR  FORCES  167 

through  space  of  the  source  emitting  the  light. 
Their  method  was  to  take  advantage  of  the 
motion  of  the  earth  itself.  A  source  of  light 
in  any  laboratory  is  moving  rapidly ;  and  by 
means  of  mirrors  one  can  throw  a  beam  of 
light  in  the  direction  of  motion  or  in  a  direc- 
tion perpendicular  to  this.  The  experiments  of 
Michelson  and  Morley  have  no  direct  bearing 
upon  the  constitution  of  matter,  or,  at  least, 
an  investigation  of  this  question  was  not  their 
purpose.  But,  using  the  accepted  hypotheses 
of  physics  and  applying  to  them  simple  math- 
ematical principles,  —  which,  of  course,  add 
nothing  of  themselves,  —  Fitzgerald  and  Lo- 
rentz  showed  that  the  immediate  consequence 
of  the  investigation  was  to  prove  that,  when 
any  body  is  moved  in  space,  its  dimensions  are 
changed  along  all  lines  in  the  body  drawn  par- 
allel to  the  motion ;  namely,  these  lines  are  all 
shortened.  So  a  body  having  a  spherical  figure 
assumes  a  spheroidal  one  owing  to  its  motion, 
its  shortest  dimension  being  in  the  direction  of 
motion ;  a  rod  is  shortened  if  moved  length- 
wise, but  the  length  is  unaffected  if  it  is  moved 


168        THE  CONSTITUTION  OF  MATTER 

sidewise,  etc.  Of  course,  these  changes  in  di- 
mension are  extraordinarily  minute  unless  the 
velocity  is  very  great.  There  can  be  no  serious 
attempt  to  explain  this  change  in  dimensions, 
this  crowding  together  of  the  molecules  — 
perhaps  accompanied  by  a  change  in  figure 
of  the  molecule  itself,  until  we  can  formulate 
the  law  for  the  forces  holding  the  molecules 
themselves  together. 

It  is  only  fair  to  state  here  that  we  can  make 
other  hypotheses  on  which  to  base  our  mathe- 
matical structure  and  so  deduce  formulae  which 
may  be  compared  with  observations  of  nature ; 
and,  if  we  adopt  those  of  Einstein,  this  ques- 
tion of  the  "Fitzgerald-Lorentz  deformation  " 
of  matter  does  not  arise.  In  the  concluding 
lecture  of  this  course  I  shall  return  to  this 
point. 


PROPERTIES    OF   METALS:  THERMIONICS; 
MAGNETISM 

IN  the  four  preceding  lectures  I  have  discussed 
what  we  may  call  the  universal  properties  of 
matter — mass  and  weight,  emission  of  radia- 
tion and  chemical  actions,  properties  common 
to  all  bodies ;  and  I  have  shown  how  far  they 
may  be  explained  as  due  to  the  existence  of 
electric  charges.  In  this  lecture,  I  wish  to  con- 
sider certain  special  properties  of  bodies,  so 
far  as  we  can  make  definite  classifications. 

In  speaking  of  the  simple  phenomena  of 
electricity,  I  defined  the  words  "conductor" 
and  "  non-conductor."  When  we  charge  two 
bodies  by  bringing  them  together  and  then 
separating  them,  we  find  that  in  some  cases 
the  attractive  power  is  limited  to  the  surface 
of  contact,  while  in  others  it  is  manifest  over 
the  entire  surface  of  the  body ;  the  latter  class 
of  bodies  are  called  "  conductors  " ;  the  former, 


170        THE  CONSTITUTION  OF  MATTER 

"non-conductors."  This  fact  of  experiment, 
enabling  us  to  divide  all  known  bodies  into 
two  groups,  evidently  points  to  a  simple  fun- 
damental property  of  matter. 

We  picture  an  atom  of  any  kind  as  con- 
sisting of  a  certain  amount  of  positive  charge 
and  an  equal  amount  of  negative  charge  in 
the  form  of  corpuscles.  We  can  easily  imagine 
bodies  electrically  neutral  but  differing  essen- 
tially in  the  manner  by  which  this  neutrality 
is  maintained.  One  type  of  body  might  be  com- 
posed of  molecules  each  individual  of  which 
is  neutral ;  the  atoms  constituting  the  molecule 
are  charged,  but  there  are  equal  amounts  of 
positive  and  negative  charges.  Another  type 
might  be  one  in  which  a  certain  proportion  of 
the  molecules  have  allowed  a  corpuscle  to 
escape  into  the  intra-molecular  spaces,  so  that 
each  such  molecule  is  positively  charged ;  but, 
of  course,  to  an  observer  on  the  outside  of 
such  a  body  there  would  be  no  evidence  of 
a  charge,  as  the  negative  corpuscles  and  the 
positive  molecules  are  so  close  together  as  to 
neutralize  each  other's  action  outside  the  body. 


CONDUCTORS  AND   NON-CONDUCTORS     171 

The  forces  of  attraction  between  corpuscles 
and  charged  molecules  would  naturally  draw 
the  former  back  into  the  molecules;  but,  if 
this  property  of  matter  is  a  natural  one,  like 
the  formation  of  ions  in  an  electrolytic  solution, 
we  must  assume  that  as  fast  as  corpuscles  re- 
combine  with  charged  molecules,  other  mole- 
cules emit  new  corpuscles ;  so  that  the  condi- 
tion of  the  body  on  the  whole  is  one  of 
statistical  equilibrium.  There  are  many  con- 
ditions like  this  in  nature,  where,  on  a  large 
scale,  everything  is  apparently  steady,  but 
really,  if  we  take  a  minute  enough  view  of  the 
phenomenon,  there  is  movement  and  change. 
Thus,  if  we  put  a  vessel  of  water  under  a  bell- 
jar,  the  water  will  evaporate ;  but,  after  a  short 
while,  we  shall  notice  that  the  volume  of  water 
ceases  to  decrease;  apparently,  the  process  of 
evaporation  has  ceased.  But  this  is  not  true. 
The  evaporation  continues ;  but  its  effect  is 
neutralized  by  the  condensation  of  the  aqueous 
vapor  on  the  surface  of  the  water;  so,  on  the 
whole,  there  is  no  gain  or  loss  in  volume  of 
the  water;  for  every  molecule  which  passes 


172         THE  CONSTITUTION  OF  MATTER 

out  of  the  water  surface  into  the  space  above 
one  descends  from  the  latter  and  is  enmeshed 
at  the  surface.  This  type  of  equilibrium  must 
exist  then  in  those  bodies  whose  molecules 
spontaneously  emit  corpuscles.  In  the  case  of 
a  solid  body  the  molecules  stay  comparatively 
fixed  in  position  and  the  corpuscles  move  to 
and  fro  at  random  in  the  space  between  the 
former.  Some  corpuscles  will  certainly  escape ; 
but,  as  they  do,  the  body  itself  becomes  charged 
positively,  thus  making  it  more  difficult  for 
other  corpuscles  to  leave  the  surface. 

When  two  bodies  are  brought  into  contact 
so  as  to  touch  over  any  surface,  it  is  an  experi- 
mental fact  that  when  separated  the  bodies 
are  charged,  one  positive,  the  other  negative, 
the  two  amounts  being  equal.  This  means  that 
the  molecules  of  one  of  the  bodies  at  the  sur- 
face of  contact  have  lost  corpuscles,  which- 
have  passed  across  to  the  contiguous  molecules 
of  the  other  body.  (This  is  simply  a  statement 
of  fact,  a  description,  not  an  explanation.)  Let 
us  now  see  what  we  should  expect  to  take 
place  if  the  body  losing  the  corpuscles  is  one 


CONDUCTORS  AND  NON-CONDUCTORS     173 

of  the  second  type  as  described  above,  that  is, 
if  it  is  made  up  of  molecules  in  kinetic  equilib- 
rium with  corpuscles.  In  this  experiment  of 
which  we  are  speaking  it  has  lost  a  certain 
number  of  corpuscles  out  through  the  surface 
of  contact  with  the  other  body,  and  then  has 
been  separated  from  the  latter.  Since  the  body 
has  lost  corpuscles,  there  will  be  a  number  of 
charged  molecules  left  uncompensated ;  so,  as 
the  random  motions  of  the  corpuscles  continue, 
they  will  serve  to  neutralize  molecules  in  the 
interior  of  the  body,  leaving  the  charged 
molecules  distributed  at  random  over  the  sur- 
face. Similarly,  let  us  suppose  that  in  the 
charging  process  this  body  has  gained  cor- 
puscles. Since  before  the  contact  with  the 
second  body  it  had  sufficient  corpuscles  mov- 
ing throughout  the  molecular  spaces  to  neu- 
tralize the  charged  molecules  present,  these 
additional  corpuscles  are  not  needed  for  this 
neutralizing  action,  and  since  we  have  assumed 
a  perfectly  random  motion  of  the  corpuscles, 
the  excess  of  these  will  be  distributed  over  the 
surface  of  the  body.  Thus,  in  both  cases  of 


174        THE   CONSTITUTION  OF  MATTER 

charging,  the  corpuscles  or  the  charged  mole- 
cules are  distributed  over  the  entire  surface 
of  the  body ;  regardless  of  where  or  how  large 
the  surface  of  contact  with  the  other  body 
was.  Such  a  body  as  this,  then,  is  what  we 
have  called  a  "conductor." 

If,  on  the  other  hand,  the  body  which  has 
gained  or  lost  the  corpuscles  is  one  which  has 
no  free  corpuscles,  but  consists  of  neutral  mole- 
cules, there  is  no  process  by  which  the  mole- 
cules modified  by  the  contact  can  be  redistrib- 
uted through  or  over  the  body,  and  therefore 
the  charged  surfaces  alone  have  charges.  Con- 
sequently, the  latter  kind  of  body  is  a  non- 
conductor. 

The  fundamental  fact  that  there  is  this  pas- 
sage of  corpuscles  across  the  contact-surface 
between  two  bodies  I  have  not  attempted  to 
explain.  It  is  easy  enough  to  describe  the 
phenomenon  in  other  words :  thus  we  may  say 
that,  whenever  there  are  two  different  mole- 
cules brought  close  together,  the  constituent 
corpuscles  are  under  the  action  of  two  forces, 
one  tending  to  attract  them  to  one  molecule, 


CONDUCTORS  175 

the  other,  to  the  second  molecule ;  the  cor- 
puscle will  therefore  move  under  the  action  of 
the  greater  force  and  attach  itself  to  the  cor- 
responding molecule.  This  is  equivalent  to 
saying  that  any  definite  molecule  may  be  con- 
sidered as  having  a  specific  attraction  for  cor- 
puscles. This,  however,  is  only  a  description 
and  is  not  to  be  thought  of  as  an  explanation. 
When  we  come  to  describe  the  internal  con- 
stitution of  atoms,  we  must  include  in  the 
conditions  to  be  satisfied  by  our  hypothetical 
atom  that  of  allowing  this  specific  attraction 
to  exist.  In  other  words,  in  picturing  the 
essential  differences  between  molecules  of  dif- 
ferent substances,  this  specific  attraction  of 
corpuscles  must  be  an  obvious  consequence  of 
our  hypotheses. 

This  conception  of  a  conductor,  given  above, 
which  may  be  considered  as  suggested  by  the 
fundamental  property  of  a  conductor  so  far 
as  charging  by  contact  is  concerned,  is  sup- 
ported by  many  other  known  facts  concerning 
conductors.  Let  us  consider  briefly  a  few  of 
these. 


176         THE  CONSTITUTION  OF  MATTER 

If  I  hold  one  end  of  a  short  metal  rod  in 
my  hand  and  place  the  other  in  a  hot  flame,  I 
am  soon  conscious  of  the  fact  that  the  end  in 
my  hand  is  becoming  hot.  In  other  words,  if 
the  temperature  of  one  end  of  a  metal  rod  is 
maintained  very  hot,  the  temperature  of  the 
other  parts  of  the  rod  is  also  raised,  the  points 
nearer  the  hot  end  having  the  higher  temper- 
ature. This  fact  is  true  of  all  bodies  to  a  cer- 
tain extent ;  but  experiments  show  that  in  the 
case  of  non-conductors,  such  as  wood,  sulphur, 
quartz,  etc.,  the  effect  is  minute  in  comparison 
with  what  it  is  in  metals,  which  are  conduc- 
tors. In  ordinary  language  we  say,  then,  that 
electrical  conductors  are  good  "heat  conduc- 
tors." Experiments  further  show  that  this  so- 
called  "conductivity  for  heat"  varies  greatly 
in  different  metals,  and  that  for  any  one  metal 
it  differs  when  different  temperatures  are 
used. 

The  best  known  property  of  a  conductor  is 
exhibited  with  reference  to  an  electric  current. 
I  have  spoken  very  hurriedly  of  this  phenom- 
enon in  a  previous  lecture;  but  it  now  demands 


CONDUCTORS  177 

a  more  detailed  description.  If  we  charge  any 
two  conductors,  say,  two  metal  plates  or  two 
metal  spheres,  one  positively  and  the  other  nega- 
tively, and  then  join  them  by  a  metal  rod  or 
wire,  we  find  that  many  changes  take  place :  the 
charges  on  the  two  conductors  will  be  altered 
(and  in  a  special  case  may  disappear) ;  the  tem- 
perature of  the  connecting  rod  or  wire  is  raised ; 
and,  while  the  change  is  going  on,  there  is  a 
magnetic  field  near  the  rod  or  wire,  i.e.,  if  a 
magnetic  needle  is  suspended  nearby,  it  will  by 
its  motions  indicate  that  it  is  under  the  action 
of  a  new  force.  All  these  actions  constitute  the 
phenomenon  which  we  describe  by  saying  there 
is  an  "  electric  current  in  the  rod  or  wire."  In 
the  experiment  described  the  effects  are  most 
transient ;  the  time  required  for  the  complete 
change  is  extremely  small.  But  owing  to  the 
discoveries  of  Volta,  Faraday  and  Seebeck  we 
have  means  of  maintaining  the  action  for  as 
long  a  time  as  we  wish.  Without  going  into 
the  full  explanation  of  the  mechanism,  I  can 
describe  one  at  least  of  the 'methods  used  for 
this  purpose.  Volta  showed  that,  if  one  dipped 


178        THE  CONSTITUTION  OF  MATTER 

a  rod  of  zinc  and  another  of  copper  into  a 
vessel  of  dilute  sulphuric  acid,  and  joined  by 
a  inetal  wire  the  two  emerging  ends  of  the 
rods,  there  was  a  continuous  electric  current 
in  the  wire  (and  also  through  the  two  metal 
rods  and  dilute  acid) :  the  temperature  of  the 
wire  is  raised  and  there  is  a  magnetic  field 
around  it.  Volta  himself  did  not  recognize 
these  two  effects ;  but  that  fact  is  unessential 
for  our  purposes.  The  heating  effect  of  a 
current  is  shown  most  obviously  by  the  or- 
dinary incandescent  electric  lamp;  and  the 
magnetic  effect  is  responsible  for  the  functions 
of  the  telegraph,  the  telephone,  the  electric 
call-bell,  and  a  hundred  instruments  in  daily 
use.  This  electric  conductivity  of  a  conductor, 
then,  is  a  most  important  property;  and  ex- 
periments have  shown  that  it  differs  greatly 
for  different  bodies  and  for  the  same  body  at 
different  temperatures. 

Other  properties  of  a  conductor  will  be  de- 
scribed presently;  but  let  us  confine  our  atten- 
tion now  to  these  two :  conductivity  for  heat 
and  for  electric  currents.  Before  offering  any 


TEMPERATURE  179 

explanation  of  them,  I  must  stop  to  state  what 
is  meant  by  temperature.  There  is  no  word,  I 
think,  in  our  language  which  is  so  much  used 
to  conceal  ignorance  as  "  heat,"  and  no  word 
about  which  there  is  so  much  confusion  of 
ideas  as  "  temperature."  Yet,  if  we  confine  our 
use  of  these  words  to  the  knowledge  that 
comes  from  daily  experiences,  there  need  not 
be  the  least  difficulty.  I  shall  avoid  the  use  of 
the  word  "heat"  and  so  shall  not  discuss  it, 
much  as  I  should  like  to ;  but  I  must  speak  of 
temperature.  We  use  the  words  "  hot "  and 
"cold"  to  describe  our  sensations  when  we 
hold  our  hands  near  a  flame  or  near  a  block 
of  ice;  and  we  say  that  the  former  has  the 
"higher  temperature." 

By  choosing  as  an  instrument  some  mate- 
rial body  and  selecting  some  property  of 
that  body  which  changes  as  the  temperature 
is  changed,  we  can  make  a  "  thermometer  "; 
and  then,  by  defining  a  scale,  e.g.,  the  Cen- 
tigrade one,  we  can  give  numbers  to  any  ther- 
mal conditions.  When  we  investigate  the  phys- 
ical differences  between  a  hot  body  and  a  cold 


180        THE  CONSTITUTION  OF  MATTER 

one,  or  when  we  learn  by  what  physical  proc- 
esses we  can  make  a  body  hotter,  we  find  that 
its  temperature  is  determined  by  the  average 
kinetic  energy  of  translation  of  the  molecules 
of  the  body,  neglecting  any  regular  systematic 
motion.  (Thus,  if  an  elastic  body,  such  as  a 
tuning-fork,  is  vibrating,  or  if  wave  disturb- 
ances are  propagated  along  a  stretched  cord, 
these  molecular  motions  are  not  included  in 
the  kinetic  energy  which  determines  tempera- 
ture.) A  good  illustration  of  this  is  offered  by 
a  gas  enclosed  in  a  cylinder  fitted  with  a  pis- 
ton. If  we  push  the  piston  in,  so  as  to  compress 
the  gas,  the  temperature  of  the  latter  is  raised, 
as  any  one  knows  who  has  blown  up  a  bicycle 
or  automobile  tire  with  a  hand-compression 
pump.  As  we  know,  the  molecules  of  the  gas 
are  in  rapid  motion,  bounding  back  and  for- 
ward; if  we  picture  to  ourselves  a  molecule  as 
it  strikes  the  piston,  it  will  be  reflected,  keep- 
ing its  speed  unchanged  if  the  piston  is  at 
rest;  but,  if  at  the  instant  when  the  molecule 
strikes  the  piston,  the  latter  is  pushed  in,  it 
will  give  an  additional  speed  to  the  molecule, 


TEMPERATURE  181 

and  therefore  the  kinetic  energy  will  be  in- 
creased. This  increased  kinetic  energy  of  the 
molecules  appeals  to  our  senses  as  a  rise  in  tem- 
perature. Similarly,  if  the  gas  expands,  push- 
ing out  the  piston,  it  does  work,  and  so  the 
average  kinetic  energy  of  the  molecules  de- 
creases ;  and  we  all  know  that,  when  a  gas 
does  expand,  its  temperature  falls,  e.g.,  as 
shown  in  the  formation  of  clouds.  Owing  to 
its  continuous  series  of  impacts  the  velocity  of 
a  molecule  of  a  gas  is  changing  every  in- 
stant; but  if  the  number  of  molecules  is 
sufficiently  large,  the  average  kinetic  en- 
ergy of  all  the  molecules  will  remain  un- 
changed unless  some  work  is  done  on  the  gas, 
e.g.,  compression ;  or  unless  the  gas  itself 
does  some  work,  e.g.,  by  expanding.  Thus 
we  see  that,  if  by  any  process  the  average 
kinetic  energy  of  translation  is  varied,  so  is 
the  temperature.  Lord  Kelvin  many  years 
ago  called  attention  to  the  fact  that  it  was  pos- 
sible to  define  temperature,  i.e.,  describe  a 
mode  of  giving  a  number  to  this  property  of  a 
body,  in  such  a  manner  as  would  be  entirely 


182        THE  CONSTITUTION  OF  MATTER 

independent  of  the  thermometric  substance 
used  in  the  measuring  instrument.  This  he 
very  properly  called  the  "  absolute  "  tempera- 
ture system.  He  also  showed  that  for  all  prac- 
tical purposes  this  system  agreed  with  the  sys- 
tem one  would  have  if  as  the  thermometer  we 
used  a  bulb  containing  a  gas  such  as  hydrogen 
or  nitrogen  and  measured  the  change  in  vol- 
ume of  the  gas,  the  pressure  on  it  being  kept 
constant  as  the  temperature  changed.  He  fur- 
ther proved  that  with  matter  as  known  to  us 
there  is  a  definite  minimum  temperature,  lower 
than  which  it  is  impossible  to  reduce  a  body ; 
this  is  called  "  absolute  zero  " ;  and  for  conven- 
ience this  is  taken  as  the  starting-point  of  the 
absolute  scale.  Thus,  when  we  speak  of  "  300 
degrees  absolute,"  we  mean  a  temperature  300 
degrees  on  the  absolute  scale  above  absolute 
zero.  (If  the  Centigrade  scale  is  used,  this  300 
degrees  absolute  is  equivalent  to  27  degrees 
above  the  temperature  of  melting  ice.) 

By  applying  our  ordinary  principles  of  me- 
chanics to  a  gas,  as  indicated  in  a  previous 
lecture,  it  is  not  difficult  to  prove  that  in  order 


TEMPERATURE  183 

to  make  the  properties  of  the  theoretical  gas 
agree  with  those  of  actual  gases,  we  must  as- 
sume that  the  average  kinetic  energy  of  trans- 
lation of  the  molecules  of  a  gas  is  proportional 
to  the  absolute  temperature,  i.e.,  the  former 
equals  the  latter  multiplied  by  a  constant  num- 
ber, this  number  being  the  same  for  all  gases. 
(This  fact  of  the  average  kinetic  energy  of  the 
molecules  being  equal  to  a  constant  multiplied 
by  the  absolute  temperature  is  also  believed  to 
be  true  of  solids  and  liquids,  the  constant  be- 
ing the  same  as  for  a  gas.) 

Now  to  return  to  our  mental  picture  of 
a  conductor  as  being  a  body  in  which  there 
is  a  state  of  statistical  equilibrium  between 
the  corpuscles  moving  freely  between  the  mol- 
ecules and  the  comparatively  stationary  mol- 
ecules.1 The  conditions  affecting  the  motions 
of  these  corpuscles  are  in  some  respects  like 
those  which  apply  to  the  molecules  of  the  gas ; 
and  Drude  made  the  bold  assumption  that  we 
may  apply  to  these  corpuscles  the  general  gas 

1  See  Thomson,  Corpuscular  Theory  of  Matter.  Lorentz,  The 
Theory  of  Electrons,  Leipzig  (1909).  Richardson,  Phil.  Mag. 
(1912). 


184        THE  CONSTITUTION   OF  MATTER 

law  connecting  temperature  and  average  kin- 
etic energy,  i.e.,  that  the  average  kinetic  en- 
ergy of  the  corpuscles  is  equal  to  the  absolute 
temperature  of  the  metal  multiplied  by  the 
same  constant  as  applies  to  gases.  Further,  the 
temperature  of  these  corpuscles  in  any  small 
portion  of  the  conductor  will  be  the  same  as 
that  of  the  molecules  themselves  in  that  por- 
tion. (We  can  compare  the  condition  of  the  free 
corpuscles  in  the  space  between  the  molecules 
with  that  of  the  molecules  of  air  in  the  empty 
spaces  in  a  porous  body.  The  air  assumes  the 
same  temperature  as  the  solid  walls  owing  to 
repeated  impacts.) 

We  can  at  once  see  how  it  is  possible,  not 
simply  to  offer  a  general  explanation  of  the 
phenomena  of  both  heat-  and  electrical  con- 
ductivity, but  also  to  apply  to  them  mathemat- 
ical analysis.  Consider  first  the  heat-phenom- 
enon. If  the  temperature  of  one  end  of  a 
metal  rod  is  raised,  the  average  kinetic  energy 
both  of  the  corpuscles  and  of  the  molecules  in 
that  end  is  increased ;  but  by  an  equilibrating 
process  of  diffusion  between  these  corpuscles 


HEAT-CONDUCTIVITY  185 

and  those  adjoining  them  farther  down  the 
rod  the  kinetic  energy  of  the  latter  is  also  in- 
creased. For  the  molecules  at  any  portion  of 
the  rod  to  be  in  equilibrium  with  the  corpus- 
cles in  their  midst,  the  temperature  must  be 
that  which  corresponds  to  the  average  kinetic 
energy  of  the  latter ;  so  we  see  how  it  is  that 
the  temperature  is  gradually  raised  down  the 
rod.  Of  course,  the  molecules  themselves  also 
play  a  part  in  this  "  diffusion  of  heat  " ;  but  it 
is  small  compared  with  the  influence  of  the  free 
corpuscles,  owing  to  the  relatively  high  veloc- 
ity of  the  latter.  Further,  if  we  can  express 
mathematically  the  rate  of  distribution  of  the 
kinetic  energy  along  the  rod,  we  can  state  all 
the  laws  of  heat-conductivity.  There  will  evi- 
dently be  differences  in  different  metals  de- 
pending upon  their  various  physical  constants ; 
and  it  is  possible  to  deduce  the  formulae  in 
terms  of  quantities  which  have  well-known 
physical  meanings. 

The  conduction  of  an  electrical  current  by 
a  metal  consists  essentially  in  the  actual  trans- 
port of  the  eorpuscles  along  the  conductor. 


186        THE   CONSTITUTION  OF  MATTER 

The  condition  required  to  produce  a  current  is 
that  there  should  be  maintained  an  electric 
force  in  a  conductor.  We  picture  the  corpus- 
cles as  attached  for  a  while  to  the  molecules, 
then  existing  free  from  them,  then  attached 
again,  etc.  During  the  intervals  of  freedom  the 
corpuscles  will  drift  under  the  influence  of 
the  impressed  electric  force,  thus  constituting 
the  current.  The  intensity  of  the  current  will 
depend  upon  the  distance  the  corpuscles  are 
moved  under  the  electric  force;  and  this  ob- 
viously is  conditioned  among  other >  things  by 
the  interval  of  time  in  which  the  corpuscles 
are  free  to  move.  The  formula  for  the  con- 
ductivity in  terms  of  the  same  physical  con- 
stants as  used  in  the  one  for  heat-conductivity 
can  be  calculated. 

We  thus  see  that  both  kinds  of  conductivity 
owe  their  mechanism  to  the  presence  of  cor- 
puscles ;  and  Drude,  Thomson,  and  Lorentz 
have  all  calculated  the  various  quantities  con- 
nected with  heat- and  electrical  conductivity 
which  admit  of  experimental  determination; 
and,  although  the  agreement  between  theory 


THERMIONICS  187 

and  fact  is  not  as  good  as  desired,  neverthe- 
less it  is  sufficiently  satisfactory  to  confirm  our 
belief  in  the  essential  features  of  the  theory. 
(When  the  number  of  free  corpuscles  for  any 
one  metal  is  calculated,  as  it  can  be  approxi- 
mately, it  is  found  to  be  different  for  different 
metals ;  it  appears  to  be  true  that  each  mole- 
cule furnishes  a  small  number.  The  total  num- 
ber, however,  is  so  large  that  a  serious  diffi- 
culty enters  when  we  consider  certain  other 
heat  properties  of  the  metals.) 

The  corpuscular  theory  of  a  metal  and  the 
assumption  of  the  connection  between  temper- 
ature and  the  kinetic  energy  of  the  corpuscles 
have  received  most  wonderful  confirmation  by 
the  experiments1  of  Professor  Eichardson,  of 
Princeton  University.  It  has  been  known  for 
many  years  that  hot  metals  had  interesting 
electrical  properties,  and  within  a  compara- 
tively recent  period  it  has  been  shown  that 
these  were  due  to  the  emission  from  the  sur- 
face of  the  metals  of  numbers  of  corpuscles. 

1  Phil  Mag.,  1908-12.  He  gives  a  summary  of  his  work 
in  Proc.  Amer.  Phil.  Soc.,  vol.  I,  p.  347  (1911). 


188         THE  CONSTITUTION  OF  MATTER 

Granting  the  presence  of  the  corpuscles  mov- 
ing to  and  fro  between  the  molecules,  it  is  an 

O  ' 

obvious  consequence  that  some  of  them  should 
escape  from  the  surface.  At  any  one  instant 
a  certain  proportion  of  the  corpuscles  will 
have  a  certain  velocity ;  and,  if  the  total  num- 
ber of  corpuscles  is  very  great,  we  can  apply 
the  theory  of  probabilities  —  just  as  Maxwell 
did  to  the  molecules  of  a  gas  —  and  thus  can 
calculate  the  relative  number  of  corpuscles 
having  various  stated  velocities  at  any  one  tem- 
perature of  the  metal.  This  Richardson  has 
done;  and,  further,  by  measuring  the  velocity  of 
the  corpuscles  as  they  escape  from  the  surface 
and  the  relative  numbers  having  different  ve- 
locities, he  has  shown  an  excellent  agreement 
between  the  two  sets  of  figures,  calculated  and 
observed.  Few  investigations  of  recent  years 
have  been  as  admirable  in  all  respects  as  this 
one  of  Richardson's;  it  combines  in  a  most 
happy  manner  keen  mathematical  ability  in 
stating  the  physical  hypotheses  and  great  ex- 
perimental skill  in  testing  the  formulae  ob- 
tained ;  and,  when  discrepancies  have  arisen 


THERMIONICS  189 

between  the  facts  of  experiment  and  predic- 
tions from  theory,  the  modification  in  the  hy- 
potheses which  he  has  made  have  been  most 
suggestive  in  other  fields. 

Kichardson  calls  the  free  corpuscles  in  a 
metal  "thermions"  and  the  branch  of  physics 
concerned  with  the  observations  of  their  prop- 
erties "thermionics."  The  importance  of  the 
subject  seems  to  justify  the  creation  of  the  new 
names,  because  the  spontaneous  emission  of 
these  corpuscles  by  metal  molecules  is  just 
as  universal  a  property  as  is  the  emission  of 
radiant  energy.  No  theory  of  thermal  or  elec- 
trical properties  of  matter  can  be  considered 
which  is  not  based  upon  these  two  character- 
istic emissions. 

An  interesting  illustration  of  the  emission 
of  corpuscles  by  a  hot  body  is  furnished  by 
the  sun.  There  can  be  no  doubt  but  that  it  is 
ejecting  these  in  enormous  quantities;  and  we 
can  best  account  for  certain  terrestrial  phe- 
nomena by  assuming  that  some  of  these  cor- 
puscles from  the  sun  ultimately  reach  the 
earth's  atmosphere. 


190        THE  CONSTITUTION  OF  MATTER 

Another  property  of  matter  which  is  ex- 
plained on  the  theory  of  the  existence  of  cor- 
puscles is  what  has  been  called  the  photo-electric 
effect.  Many  metals  which  at  ordinary  temper- 
atures emit  comparatively  few  corpuscles  lose 
them  in  large  numbers  if  light  falls  upon  the 
surface;  and  many  if  not  all  non-conductors 
do  the  same.  Whatever  concept  we  may  have 
of  the  nature  of  radiant  energy,  it  is  a  fact 
that  it  consists  of  a  certain  condition  which 
exerts  a  force  upon  any  electric  charge.  The 
radiation  is  produced  by  oscillations  of  charges, 
and  when  it  falls  upon  a  charge  it  exerts  a 
force  upon  it.  Thus,  as  the  radiant  energy 
from  the  sun  or  from  an  arc  light  or  a  spark 
falls  upon  a  body,  the  corpuscles  in  the  latter 
will  be  given  additional  motion;  and,  if  the 
velocity  attained  is  sufficient,  they  will  be  able 
to  escape  from  the  surface.  The  experimental 
investigation  of  this  photo-electric  effect  has 
been  one  of  the  most  interesting  of  recent 
years;  and  there  still  remain  many  points 
which  require  further  study.  All  experiments 
go  to  prove  that  these  ejected  corpuscles  are 


PHOTO-ELECTRIC  ACTION  191 

not  "free"  ones,  but  those  forming  part  of 
molecules. 

Owing  to  the  accelerations  of  the  free  cor- 
puscles in  metals  there  is,  of  course,  an  emis- 
sion of  radiant  energy.  Some  of  this  emerges 
into  the  space  outside  the  body,  giving  rise 
to  the  characteristic  continuous  spectrum  of  a 
solid  body ;  but  part  of  this  energy  emitted  by 
any  one  corpuscle  is  also  received  by  other 
corpuscles.  So  the  effect  of  this  internal  radi- 
ation is  the  same  as  that  of  energy  penetrating 
from  without ;  and  we  might  expect  therefore 
that  part  of  the  spontaneous  emission  of  cor- 
puscles by  metals  is  in  reality  due  to  an  inter- 
nal photo-electric  action. 

We  get  evidence  of  photo-electric  action  of 
another  kind  in  the  action  of  light  upon  se- 
lenium. This  substance  has  most  interesting 
chemical  and  physical  properties,  and  is  known 
to  exist  in  several  forms,  the  molecular  group- 
ings of  which  are  not  yet  clearly  understood. 
In  one  of  these  forms  it  is  a  very  poor  electric 
conductor ;  but,  if  light  falls  upon  it,  its  con- 
ducting properties  are  increased.  The  explana- 


192         THE  CONSTITUTION  OF  MATTER 

tion  of  this  phenomenon,  which  has  been 
offered  by  Dr.  A.  H.  Pfund1  and  which  is 
most  satisfactory,  is  that  the  radiation  pene- 
trating into  the  selenium  ionizes  the  molecules, 
causing  the  emission  of  corpuscles  which  have 
all  the  properties  of  free  ones  so  long  as  the 
light  is  being  absorbed. 

The  most  obvious  difference  between  a  con- 
ductor and  a  non-conductor  lies  in  the  fact 
that,  for  all  general  purposes,  a  solid  conductor 
is  opaque  to  light,  while  a  non-conductor  is 
transparent.  Of  course,  neither  statement  is 
absolutely  correct;  if  a  piece  of  metal,  e.g., 
gold,  is  beaten  out  into  a  thin  film,  it  is  trans- 
parent to  greenish-blue  light;  ordinary  glass 
is  absolutely  opaque  to  certain  light-waves; 
sulphur  and  pitch  are  opaque  to  ordinary  light. 
But  on  the  whole,  the  distinction  is  a  good 
one ;  and  all  metals  are  absolutely  opaque  to 
all  types  of  light  unless  they  are  made  in  ex- 
tremely thin  films.  The  reason  is  not  far  to 
seek.  When  radiant  energy  falls  upon  a  metal, 
the  free  corpuscles  are  given  additional  motion ; 
1  Phys.  Rev.,  vol.  xxvm,  p.  324  (1909). 


OPACITY  OF  METALS  193 

this  requires  work;  and  consequently  the 
amount  of  radiant  energy  which  penetrates 
into  the  metal  is  continuously  decreased.1  It 
is  evident  that  this  is  true  for  radiant  energy 
of  every  kind.  But  in  addition  to  the  free 
corpuscles,  all  metals  have,  of  course,  the  cor- 
puscles which  form  part  of  the  atoms  in  the 
molecules.  These  we  may  call  "bound  ";  and, 
whatever  is  our  conception  of  the  structure  of 
the  atom,  we  picture  these  bound  corpuscles  as 
capable  of  emitting  radiation  having  definite 
periodicities,  characteristic  of  the  kind  of 
matter.  Then,  as  the  radiant  energy  which  we 
call  light  falls  upon  the  molecules  in  the  outer 
surface  of  the  metal,  these  bound  corpuscles 
will  be  given  additional  energy,  by  a  process 
of  resonance;  and,  if  they  remove  a  large 
amount  of  energy  from  the  incident  radiation, 
the  latter  will  penetrate  only  a  short  distance 
into  the  metal.  Similarly,  non-conductors  are 
made  up  of  molecules  which  contain  bound 
corpuscles — practically  no  others;  but  there 
is  this  essential  difference  between  the  two 

1  See  Wood,  Physical  Optics,  new  edition,  1911. 


194         THE  CONSTITUTION  OF  MATTER 

bodies,  conductors  and  non-conductors :  in  the 
former  the  bound  corpuscles  can  escape  with 
comparative  ease,  as  is  shown  by  the  properties 
we  have  been  discussing ;  in  the  latter,  they 
cannot  escape  except  under  most  strenuous 
conditions.  Speaking  in  a  general  manner, 
this  means  then  that  the  bound  corpuscles  of 
a  metal  can  be  moved  much  more  easily  than 
those  of  a  non-conductor ;  and  therefore  in  the 
case  of  the  former  the  incident  radiant  energy 
will  be  taken  up  by  a  very  thin  layer  of  mole- 
cules, while  in  a  non-conductor  a  much  greater 
thickness  is  required.  Further,  owing  to  the 
difference  in  the  extent  to  which  the  bound 
corpuscles  respond  in  the  two  cases,  and  since 
this  absorption  must  be  a  resonance  process, 
there  will  be  absorption  by  the  non-conductor 
only  if  the  incident  radiant  energy  contains 
periodicities  equal  to  those  of  the  bound  cor- 
puscles. In  other  words,  the  non-conductor 
absorbs  only  in  a  "selective"  manner,  while 
the  conductor  absorbs  all  radiation;  but  its 
selective  action  is  so  intense  that  it  takes  place 
in  the  "  skin  "  only.  Owing  to  this  fact,  that 


METALLIC   REFLECTION  195 

practically  all  of  the  absorption  of  the  radiant 
energy  by  the  bound  corpuscles  of  a  conductor 
takes  place  in  a  layer  containing  only  a  few 
molecules,  the  added  motion  of  these  corpuscles 
will  all  be  practically  identical;  and  therefore 
their  combined  motion  will  give  rise  to  a  re- 
flected disturbance  of  the  period  characteristic 
of  them.  Radiant  energy  of  a  definite  period 
produces  a  definite  color-sensation,  provided 
the  period  lies  within  certain  limits ;  and  thus 
we  see  why  it  is  that  metals  have  characteristic 
colors,  which  are  marked  by  a  great  intensity. 
On  the  other  hand,  when  radiant  energy  pen- 
etrates a  non-conductor  and  is  absorbed,  a 
thick  layer  of  molecules  is  required ;  and  there- 
fore there  is  not  any  agreement  in  the  nature 
of  the  vibrations  of  the  corpuscles  at  differ- 
ent depths;  consequently  they  cannot  react 
together  and  produce  an  emergent  reflected 
disturbance  —  some  of  the  corpuscles  will  be 
vibrating  in  one  direction,  others  in  the  oppo- 
site, etc.  (This  condition  is  not  unlike  the 
state  of  affairs  if  a  pendulum  is  struck  a  number 
of  random  blows  from  all  directions,  and  as  a 


196        THE  CONSTITUTION  OF  MATTER 

consequence  there  is  no  resultant  motion.)  The 
energy  absorbed  by  the  corpuscles  of  a  non- 
conductor, in  general,  ultimately  becomes  dis- 
tributed among  the  molecules,  and  is  shown 
by  a  rise  of  temperature  or  some  other  heat- 
effect. 

I  have  spoken  of  non-conductors  as  if  they 
were  composed  entirely  of  neutral  molecules ; 
but  the  fact  should  be  noted  that  when  the 
temperature  is  sufficiently  high,  many  non- 
conductors are  able  to  conduct  electric  cur- 
rents. 

The  corpuscular  theory  of  metals  which  I 
have  given  is  not  the  only  one  which  can  be 
devised  to  account  for  the  experimental  facts ; 
and,  in  fact,  Thomson  has  developed  a  theory 
along  other  lines,  which  in  its  deductions  is 
free  from  some  of  the  objections  raised  against 
the  simpler  theory.  It  is  most  probable  that 
the  complete  theory  of  the  properties  of  a 
metal  will  require  us  to  take  into  account  not 
alone  the  free  corpuscles  but  also  the  bound 
ones  inside  the  molecules ;  it  would  be  very 
remarkable  if  this  were  not  so. 


MAGNETISM  197 

There  are  many  other  properties  of  metals, 
as  distinct  from  non-conductors,  which  have 
been  discovered  from  time  to  time  and  have 
been  investigated  by  many  people.  Chief  of 
these  are  the  various  phenomena  of  thermo- 
electricity and  those  associated  with  the  Hall 
effect.  These  are  described  in  full  in  the  more 
modern  textbooks  of  physics ;  and  Thomson 
and  Richardson  have  shown  how  the  main 
phenomena  can  be  deduced  as  consequences 
of  the  corpuscular  theory.  There  are  great 
difficulties  it  is  true ;  but  still  every  one  be- 
lieves that  the  great  conception  of  free  cor- 
puscles will  serve  as  a  basis  for  the  complete 
explanation  of  all  metallic  phenomena. 

This  lecture  cannot  be  concluded  without 
saying  a  few  words  about  magnetism.  A  piece 
of  matter  is  called  a  "  magnet  "if  it  has  the 
power  to  attract  iron  —  excluding,  of  course, 
any  such  action  due  to  gravitation  or  electri- 
fication. Some  ores  as  found  in  mines  are  mag- 
nets ;  but  most  of  us  are  accustomed  to  see 
magnets  in  the  form  of  steel  bars  or  lozenge- 
shaped  "needles."  Such  a  magnet  has  the 


198         THE  CONSTITUTION  OF  MATTER 

power  to  attract  not  only  iron  but  nickel,  co- 
balt, and  a  few  other  substances,  all  of  which 
are  called  "  magnetic."  The  subject  of  mag- 
netism has  been  for  centuries  the  object  of 
scientific  investigations ;  and  at  the  present 
time  we  know  many  facts  of  great  importance 
concerning  its  manifestations.  One  of  these  is 
that  each  minute  part  of  a  magnetic  substance 
is  itself  a  magnet,  with  its  north  and  south 
"  poles,"  and  that  by  no  means  in  our  control 
are  we  able  to  separate  the  two  poles.  In  short, 
we  seem  to  be  justified  in  saying  that  each 
molecule  of  a  magnetic  substance  is  a  magnet 
itself.  In  this  connection  Professor  Weiss  of 
Paris  has  made  a  most  important  discovery.1 
He  has  shown  that  the  magnetic  strengths  of 
the  elementary  magnets  of  all  the  magnetic 
substances  are  multiples  of  the  same  quantity. 
That  is,  calling  the  ultimate  magnet  a  "  mag- 
neton," the  elementary  magnet  of  one  sub- 
stance may  be  equivalent  to  two  magnetons, 
that  of  another  to  ten,  etc. 

The  fact  which  demands  explanation,  how- 

1  Journal  de  Physique  (v),  vol.  I,  pp.  900,  965  (1911). 


MAGNETISM  199 

ever,  is  the  existence  of  the  magneton,  or,  if 
this  investigation  of  Weiss's  is  not  considered 
conclusive,  the  existence  of  any  elementary  or 
molecular  magnet.  Ampere  showed,  nearly 
one  hundred  years  ago,  that,  if  there  were  an 
electric  current  flowing  in  a  molecule,  the  lat- 
ter would  have  the  properties  required  for 
magnetism  ;  but  this  simply  states  the  prob- 
lem in  a  different  manner.  This  point  of  view 
has,  however,  one  great  advantage  when  we 
consider  molecules  and  atoms  as  containing 
corpuscles ;  because,  if  there  are  inside  the 
atoms  corpuscles  or  rings  of  corpuscles  in  rapid 
rotation,  this  condition  is  in  all  respects  equiva- 
lent to  an  electric  current.  Bearing  this  fact 
in  mind,  Langevin1  and  others  have  developed 
theories  of  magnetism  which  are  to  a  certain 
extent  satisfactory.  There  are,  however,  great 
difficulties  which  are  not  yet  entirely  over- 
come. One  is  the  fact  that  there  is  a  well- 
known  alloy  of  copper,  aluminium  and  man- 
ganese —  all  non-magnetic  elements  —  which 
is  itself  markedly  magnetic. 

1  Ann.  Chem.  et  Phys.,  Ser.  vm,  vol.  V,  p.  70  (1905). 


VI 

MODELS  OF  ATOMS;   CONCLUSIONS 

LET  us,  as  an  introduction  to  this  the  conclud- 
ing lecture,  summarize  what  we  have  learned 
in  the  preceding  lectures,  so  as  to  see  to  what 
point  our  theory  and  our  knowledge  of  experi- 
ments have  brought  us. 

We  have  discussed  the  mass  and  weight  of 
matter,  the  emission  of  radiant  energy  by  all 
bodies,  the  subdivision  of  matter  into  mole- 
cules and  atoms  and  the  converse  processes  — 
the  combination  of  atoms  to  form  molecules, 
and  the  grouping  of  molecules  to  form  ex- 
tended bodies,  and  the  general  subdivision  of 
all  bodies  into  conductors  and  non-conductors; 
we  have  shown  that  part  at  least  of  the  mass 
of  a  body  may  be  attributed  to  the  existence 
of  positive  and  negative  charges  in  the  atoms, 
which  we  proved  were  present ;  we  have  of- 
fered as  an  explanation  of  gravitation  a  certain 
law  of  force  between  these  electric  charges  in 


MODELS  OF  ATOMS  201 

the  atoms ;  we  have  shown  how  radiant  energy 
is  due  to  acceleration  of  corpuscles ;  and  finally 
we  have  explained  radio-activity,  chemical 
combinations,  and  the  distinctive  properties 
of  conductors  as  due  to  certain  stable  and  un- 
stable arrangements  of  corpuscles  in  combina- 
tion with  the  corresponding  positive  charge. 

What  remains  to  be  done,  therefore,  is  to 
devise  a  model  of  corpuscles  and  positive 
charge  which  will  have  the  requisite  properties 
of  stability  and  of  variability  required  for  the 
different  assumptions  made,  and  will  in  addi- 
tion offer  the  possibility  of  explanation  of  the 
periodicity  which  atoms  of  different  elements 
show,  as  was  stated  in  the  first  lecture.  The 
only  one  who  has  attacked  this  problem  with 
any  success  is  Thomson.  In  the  "  Philosophi- 
cal Magazine  "  of  March,  1904,  he  published 
his  epoch-making  article  on  this  subject.  Since 
then  he  has  not  seriously  modified  his  funda- 
mental idea;  and  but  few  additions  worthy 
of  note  have  been  made  by  others.1 

Bearing   in  mind  the  fact   that   negative 

1  See  the  references  on  p.  214. 


202         THE  CONSTITUTION  OF  MATTER 

charges  always  occur  in  the  form  of  corpuscles 
and  that  no  smaller  positive  charge  than  the 
hydrogen  atom  has  ever  been  obtained,  Thom- 
son proposed  as  the  fundamental  structure  of 
all  atoms  a  comparatively  large  positive  nu- 
cleus consisting  of  a  sphere  in  which  positive 
electricity  is  uniformly  distributed  and  inside 
of  which  are  placed  the  corpuscles,  arranged 
in  such  a  geometrical  configuration  as  to  make 
the  entire  atom  stable. 

For  simplicity  of  mathematical  treatment 
Thomson  assumed  that  the  corpuscles  were 
arranged  at  equal  intervals  around  the  cir- 
cumferences of  circles,  all  of  these  having  as  a 
common  centre  that  of  the  sphere  and  all  lying 
in  one  plane.  Thus  a  certain  number  of  cor- 
puscles lie  in  one  circle  of  a  comparatively 
small  radius,  distributed  at  equal  intervals ;  a 
certain  number  lie  in  a  different  circle  outside 
the  first  one,  and  also  equally  distributed,  al- 
though the  interval  between  them  need  not  be 
the  same  as  in  the  former  circle,  etc. 

We  see,  then,  that  the  corpuscles  consti- 
tuting any  ring  are  repelled  outward,  away 


MODELS   OF  ATOMS  203 

from  the  centre,  by  their  mutual  interaction, 
since  they  are  all  charged  alike ;  but  the  action 
of  the  positive  electrification  is  to  draw  them 
in  the  opposite  direction,  back  towards  the 
centre.  Consequently,  if  they  are  in  equilib- 
rium, these  two  forces  must  balance  each 
other.  This  is  of  course  true  if  we  assume  the 
ring  of  corpuscles  to  be  at  rest ;  but,  if  it  is 
rotating  in  its  own  plane,  so  that  each  corpus- 
cle is  moving  in  a  circle,  an  additional  force 
is  required,  directed  towards  the  centre  — just 
as  the  force  of  gravitation  acting  on  the  moon 
is  required  to  make  it  move  in  a  circle  around 
the  earth.  Consequently,  in  this  case  of  rota- 
tion the  arrangement  of  the  corpuscles  must 
be  such  that  the  attraction  due  to  the  positive 
electrification  exceeds  the  repulsion  owing  to 
the  interaction  of  the  corpuscles  themselves 
by  an  amount  sufficient  to  maintain  the  rota- 
tion. 

This  particular  model  of  an  atom  was  se- 
lected by  Thomson  only  because  of  the  ease 
with  which  the  mathematical  difficulties  could 
be  solved.  As  he  says,  the  object  is  to  show 


204         THE  CONSTITUTION  OF  MATTER 

that  stable  arrangements  of  corpuscles  will 
have  many  properties  in  common  with  real 
atoms  and  this  special  case  is  chosen  solely  on 
the  ground  of  simplicity.  "  The  number  of 
corpuscles  corresponding  to  any  particular 
property  would  doubtless  be  different  if  we 
took  a  three-  instead  of  a  two-dimensional  dis- 
tribution of  corpuscles,  or  if  instead  of  sup- 
posing the  attractive  force  exerted  by  the  pos- 
itive electricity  to  vary  directly  as  the  distance 
from  a  fixed  point  we  assumed  that  the  den- 
sity of  the  positive  electricity  inside  the  sphere 
was  not  uniform." 

In  making  his  actual  calculations  for  the 
possible  configuration  of  circular  rings  of  cor- 
puscles Thomson  assumed  that  these  were  at 
rest ;  but  in  discussing  the  properties  of  these 
atomic  models  he  showed  how  it  was  necessary 
to  assume  rotations  in  order  to  secure  stabil- 
ity and  also  to  illustrate  the  properties  of 
actual  atoms.  If  a  definite  rotation  is  required 
for  stability,  we  can  easily  understand  that, 
if  owing  to  radiation  of  energy,  the  velocity 
of  this  rotation  decreases,  the  force  of  attrac- 


MODELS  OF  ATOMS  205 

tion  towards  the  centre  may  be  sufficient  to 
cause  an  internal  explosion. 

The  simplest  type  of  atom  would  be  one  in 
which  there  was  a  single  corpuscle  placed  at 
the  centre  of  the  atom;  and  the  next  simplest 
that  in  which  all  the  corpuscles  are  in  one 
ring ;  and  Thomson  investigated  mathemati- 
cally the  conditions  of  stability  when  there  were 
two,  three,  etc.,  corpuscles  in  the  ring.  He 
showed  that,  as  the  number  was  increased, 
there  came  a  time  when  the  criterion  of  sta- 
bility required  that  the  last  corpuscle  added  be 
placed  at  the  centre  of  the  sphere  rather  than 
in  the  original  ring ;  and  that,  as  two,  three, 
etc.,  more  were  added,  the  condition  of  sta- 
bility required  these  to  be  arranged  in  an  inner 
concentric  circle.  Thus,  if  the  number  of  cor- 
puscles is  very  large,  the  most  stable  arrange- 
ment would  be  one  in  which  there  are  several 
such  rings.  Of  course,  in  working  out  these  dis- 
tributions of  corpuscles  due  attention  was  paid 
to  the  need  of  having  the  quantity  of  positive 
charge  equal  to  that  of  the  total  negative 
charge  for  any  definite  number  of  corpuscles. 


206        THE  CONSTITUTION  OF  MATTER 

It  is  evident  that,  if  we  work  out  the  stable 
configurations  for  one,  two,  three,  etc.,  up  to 
a  large  number  of  corpuscles,  there  will  be 
shown  a  definite  periodicity.  Thus,  consider 
an  atom  containing  simply  a  ring  with  three 
corpuscles ;  there  will  be  another  atom  contain- 
ing three  corpuscles  in  an  inner  ring  and  ad- 
ditional ones  in  an  outer  ring ;  there  will  also 
be  another  containing  still  added  corpuscles  in 
a  second  outer  ring,  etc.  In  this  way  we  see 
how  it  is  possible  to  account  for  different  atoms 
and  also  for  the  periodicities  which  we  have 
shown  exist  between  atoms  of  different  ele- 
ments. Thus,  the  following  is  an  illustration  of 
the  stable  arrangements  found  starting  with  a 
nucleus  of  a  ring  of  five  corpuscles :  (a)  five 
corpuscles  in  a  ring;  (6)  five  in  an  inner  ring, 
eleven  in  an  outer ;  (c)  five  in  one  ring,  eleven 
in  one  outside  this,  fifteen  in  the  outmost ; 
(d)  five  in  one  ring,  eleven  in  the  next,  fifteen 
in  the  next,  seventeen  in  the  outmost  \  (e)  the 
same  as  the  preceding  with  an  outer  ring  of 
twenty-one  added,  etc.  It  is  very  evident  that 
we  have  here  a  periodicity ;  and  if  any  definite 


MODELS  OF  ATOMS  207 

physical  property  is  characteristic  of  a  ring  of 
five  corpuscles,  this  will  appear  in  all  the 
atoms  mentioned  —  modified,  of  course,  by 
the  presence  of  the  other  rings.  There  are 
similar  groups  of  atoms  having  as  a  nucleus  a 
ring  of  four  corpuscles,  etc.  Such  a  group  of 
atoms  all  having  the  same  inmost  circle  of 
corpuscles  corresponds  to  a  "  column "  in  the 
periodic  system  of  the  atoms  of  the  elements. 
Any  one  interested  in  the  numerical  distribu- 
tion of  corpuscles  in  rings  can  find  all  the 
facts  given  in  Thomson's  writings. 

Thomson  also  investigated  in  this  connec- 
tion a  problem  which  in  some  respects  is  more 
important  than  the  fundamental  one  just  dis- 
cussed. That  was  this :  Given  a  neutral  atom 
consisting  of  the  positive  sphere  and  the  asso- 
ciated rings  of  corpuscles,  will  the  system  still 
be  stable  if  a  corpuscle  is  added  or  removed  ? 
—  and  by  how  much  relatively  is  the  poten- 
tial energy  of  the  system  changed  by  either 
of  these  steps  ?  This  problem  we  see  is  differ- 
ent from  the  preceding  one,  because  in  this  the 
atom,  modified  by  the  addition  or  removal  of 


208        THE  CONSTITUTION  OF  MATTER 

a  corpuscle,  is  no  longer  electrically  neutral; 
and  it  evidently  is  fundamental  in  discussing 
the  explanation  of  the  formation  of  mole- 
cules. 

With  the  assumptions  made  as  to  the  ar- 
rangement of  the  corpuscles  in  circles,  Thom- 
son found  that  the  simplest  atom  would  be 
one  having  a  single  corpuscle  at  the  centre, 
the  next  simplest  then  would  have  two  corpus- 
cles in  a  ring,  the  next  three,  etc. ;  up  to  an 
atom  having  five  corpuscles  in  a  single  ring; 
then,  if  there  are  six  corpuscles,  the  theory 
demands  five  corpuscles  in  a  ring  and  one  at 
the  centre,  etc.  When  the  number  of  corpus- 
cles is  large,  so  that  there  are  several  rings, 
there  will  be  several  atoms  all  of  which  have 
the  same  number  of  corpuscles  in  the  outmost 
ring.  Thus  the  nine  atoms  having  from  fifty- 
nine  to  sixty-seven  corpuscles  all  have  twenty 
in  the  outer  circle.  These  nine  atoms  we  can 
call  a  "  row."  Thomson  showed  that  the  atom 
at  the  left-hand  end,  having  fifty-nine  corpus- 
cles, is  comparatively  unstable  and  can  easily 
lose  a  corpuscle,  but  that,  if  it  does  so,  it  will 


MODELS  OF  ATOMS  209 

owing  to  its  positive  charge  attract  to  itself 
another  corpuscle,  and  so  return  to  its  pre- 
vious condition.  On  the  other  hand,  if  a  cor- 
puscle is  added  to  this  atom,  it  is  stable ; 
similarly,  if  two,  three,  etc.,  up  to  eight  cor- 
puscles are  added.  Thus,  this  atom  would  be 
considered  as  electro-positive,  having  a  valency 
of  zero ;  but  in  a  molecule  where  it  is  com- 
bined with  an  atom  more  electro-positive  than 
itself  it  might  reach  a  valency  of  eight.  The 
atom,  having  sixty  corpuscles,  can,  under  the 
disturbing  influence  of  other  charged  atoms, 
lose  one  corpuscle  and  still  be  stable ;  but  if 
it  loses  two,  it  will  attract  back  one ;  thus  it  is 
electro-positive  and  has  a  valency  one ;  it  is 
possible  for  it  to  be  stable  also  if  we  add  to  it 
one  or  more,  up  to  seven,  corpuscles;  thus 
it  is  possible  for  it  to  have  a  valency  seven  in 
certain  molecules.  Similarly,  the  atom  having 
sixty-one  corpuscles  is  more  stable  than  the 
two  before  it,  but  under  disturbing  actions  it 
may  lose  two  corpuscles ;  and,  if  it  does,  it  will 
still  be  stable ;  it  is,  therefore,  electro-positive 
and  has  a  valency  of  two.  Considering  the 


210        THE   CONSTITUTION  OF  MATTER 

atoms  at  the  other  end  of  the  row,  the  one 
having  sixty-seven  corpuscles  is  extremely  sta- 
ble, so  that  corpuscles  could  be  removed  only 
with  difficulty ;  but  it  would  be  possible  for  it 
to  lose  one,  two,  etc.,  up  to  eight,  and  still  be 
stable;  and,  if  a  corpuscle  were  to  be  added, 
it  would  not  keep  it.  Therefore,  as  an  electro- 
positive atom  it  would  have  a  valency  of  eight, 
and  as  an  electro-negative  one,  a  valency  of 
zero.  The  atom  before  it,  having  sixty-six 
corpuscles,  would,  if  any  opportunity  offered, 
attach  a  single  corpuscle  and  would  then  be 
very  stable ;  but  the  addition  of  two  would 
make  it  unstable ;  therefore,  it  would  be  an 
electro-negative  atom  having  a  valency  one. 
It  could,  however,  be  made  to  lose  one,  two, 
etc.,  up  to  seven,  corpuscles,  and  would  still 
be  stable ;  thus,  in  a  molecule  with  an  atom 
more  electro-negative,  it  might  have  a  valency 
seven,  etc. 

The  same  facts  appear  in  regard  to  the 
atoms  in  any  one  row.  Let  us  now  compare 
them  with  the  actual  chemical  atoms.  Two  of 
the  rows  of  the  periodic  table  are :  — 


MODELS  OF  ATOMS  211 

O  V  •>  (J 

(1)  Helium  —  Lithium  —  Beryllium  —  Boron  —  Car- 
bon —  Nitrogen  —  Oxygen  —  Fluorine  —  Neon. 

(2)  Neon — Sodium — Magn esium — Aluminium — Sili- 
con —  Phosphorus  —  Sulphur  —  Chlorine  —  Argon. 


At  the  left-hand  ends,  Helium  and  Neon 
have  a  valency  zero  ;  Lithium  and  Sodium  are 
strongly  electro-positive  and  have  a  valency 
one ;  Berylliumand  Magnesium  are  also  electro- 
positive and  have  a  valency  two,  etc.  At  the 
other  end,  Neon  and  Argon  have  a  valency 
zero ;  Fluorine  and  Chlorine  are  strongly  elec- 
tro-negative with  a  valency  one,  etc.  Iodine, 
which  comes  in  the  same  column  as  Fluorine 
and  Chlorine,  is  electro-negative  with  a  valency 
one,  as  in  the  molecule  hydriodic  acid,  HI ;  but 
when  combined  with  Chlorine,  an  atom  more 
electro-negative  than  itself,  it  has  a  valency 
five,  as  shown  in  the  molecule  IC15. 

We  thus  see  how  wonderfully  Thomson's 
model  of  atoms  allows  one  to  explain  the  fact 
that  some  atoms  are  electro-positive  and  others 
electro-negative  and  also  the  existence  of 
valency.  It  is  specially  interesting  to  note  also 
that  the  fact  of  an  atom  having  different  val- 


212        THE  CONSTITUTION  OF  MATTER 

encies  in  different  types  of  molecules  is  ex- 
plained. Thomson  showed  also  that  his  model 
of  an  atom  would  explain  many  other  well- 
known  facts  of  chemistry,  notably  the  proper- 
ties of  unsaturated  compounds  and  of  those 
compounds  of  Carbon  which  show  asymmetry. 
When  we  consider  the  simplicity  of  the  as- 
sumptions, the  agreement  between  their  con- 
sequences and  the  phenomena  of  Chemistry  is 
such  as  to  lend  strong  support  to  the  corpus- 
cular theory  of  matter. 

We  can  also  obtain  a  general  impression  as 
to  the  essential  difference  between  a  metal  and 
a  non-metal,  as  shown  by  the  facts  of  electrical 
conductivity,  the  emission  of  corpuscles,  etc. 
All  metals  would  correspond  to  those  types 
of  Thomson's  atoms  which  can  lose  corpuscles 
with  comparative  ease ;  so  that  in  a  collection  of 
molecules  made  up  of  such  atoms  there  might 
well  be  what  may  be  called  an  evaporation  of 
corpuscles  into  the  intramolecular  spaces.  We 
should  then  have  these  free  corpuscles,  in 
addition  to  the  bound  ones  inside  the  atoms. 

The  process  by  which  a  radio-active  atom 


MODELS  OF  ATOMS  213 

loses  corpuscles  and  alpha  particles  must  un- 
doubtedly be  more  of  an  explosive  nature  than 
is  this  spontaneous  emission  of  corpuscles  in- 
side metals.  This  has  been  explained  as  due 
to  the  loss  of  energy  of  the  ring  of  corpuscles 
and  its  consequent  decrease  in  velocity  of  ro- 
tation. If  this  is  great  enough  the  atom  may 
become  unstable ;  because,  if  the  velocity  of 
revolution  of  the  corpuscles  becomes  too  small, 
the  electric  forces  will  disrupt  the  ring ;  then 
owing  to  this  instability  there  would  be  a 
rearrangement  of  parts  inside  the  atom;  and, 
if  the  process  is  sufficiently  violent,  parts  of 
the  atom  may  be  ejected.  By  an  internal 
change  like  this  we  can  account  for  the  emis- 
sion of  both  alpha  and  beta  particles ;  and  the 
evidence  is  fairly  conclusive  that  the  gamma 
rays  are  in  general  a  consequence  of  the  emis- 
sion of  the  corpuscles  which  constitute  the 
beta  particles.  This  explanation  of  the  trans- 
formation of  a  radio-active  atom  cannot,  how- 
ever, be  regarded  as  satisfactory  ;  because  this 
change  is  independent  of  the  age  of  the  atom, 
and  obeys  simply  the  law  of  probability. 


214         THE  CONSTITUTION  OF  MATTER 

The  question  as  to  whether  the  positive 
electrification  of  the  atom  is  distributed  uni- 
formly or  gathered  in  particles  has  been  raised ; 
but  the  experiments1  of  J.  R.  Crowther  on  the 
transmission  of  Roentgen  radiation  through 
various  substances  seem  to  prove  that  it  is 
uniform. 

Of  course,  as  Thomson  made  clear  in  his 
first  paper,  one  must  not  attach  too  much  im- 
portance to  the  simple  hypothesis  made  as  to 
the  distribution  of  the  corpuscles ;  many  other 
stable  configurations  can  be  imagined. 

Quite  recently2  a  modification  of  Thomson's 
hypothesis  has  been  made  by  H.  A.  Wilson. 
He  considers  each  corpuscle  as  being  electric- 
ally saturated  by  the  positive  electrification  in 
a  small  sphere  at  the  centre  of  which  is  the 
corpuscle,  so  that  each  of  these  spheres  is  elec- 

1  Proc.  Roy.  Soc.,  vol.  LXXXIV,  p.  226  (1911).  See  also  two 
papers  by  Rutherford,  Phil.  Mag.,  vol.  xxi,  p.  669  (1911); 
vol.  xxiv,  p.  453  (1912).  Nagaoka,  in  the  Phil  Mag.,  vol. 
vn,  p.  445  (1904),  discussed  the  stability  of  an  atom  con- 
sisting of  a  minute  positive  nucleus  surrounded  by  rings  of 
corpuscles. 

2  Proc.  Amer.  Phil.  Soc.,  vol.  I,  p.  366  (1911).  Phil.  Mag., 
vol.  xxi,  p.  718  (1911). 


MODELS  OF  ATOMS  215 

trically  neutral.  Thus  the  problem  becomes  a 
geometrical  one  of  dividing  the  large  atomic 
sphere  into  a  number  of  equal  volumes  equal 
to  the  number  of  corpuscles,  each  small  vol- 
ume being  as  nearly  spherical  as  possible. 
Taking  the  elements  in  any  one  column  of  the 
periodic  system,  he  considers  that  each  atom 
is  formed  from  the  one  before  it  by  the  addi- 
tion of  a  spherical  layer  containing  a  whole 
number  of  the  small  equal  elements  of  volume. 
Thus,  beginning  with  different  nuclei,  differ- 
ent atoms  can  be  built  up ;  and,  assuming  that 
the  mass  of  an  atom  is  proportional  to  the 
number  of  corpuscles,  we  can  develop  the 
theory.  On  comparing  this  with  the  relative 
masses  of  the  chemical  atoms  a  very  remark- 
able agreement  is  found ;  and  a  most  interest- 
ing consequence  is  that  the  actual  number  of 
corpuscles  in  a  hydrogen  atom  is  eight ;  and 
the  number  in  other  atoms  is  therefore  known. 
Let  us  now  see  how  far  the  Thomson  atom 
does  explain  the  properties  of  matter.  The 
main  facts  of  chemistry  are  accounted  for  in 
an  admirable  manner ;  so  are  those  concerned 


216        THE  CONSTITUTION  OF  MATTER 

with  metals ;  and  mass  and  gravitational  forces 
follow  naturally.  The  most  important  fact  not 
yet  specifically  discussed  is  the  emission  of 
radiant  energy.  If  we  picture  this  as  due  to 
the  periodic  motions  of  the  bound  corpuscles 
in  the  atoms,  grave  difficulties  arise,  some  of 
which  havebeen  mentioned  in  a  previous  lecture. 
There  is,  however,  a  great  deal  of  evidence  to 
support  the  belief  that  radiant  energy  is  emitted 
only  when  what  we  call  chemical  action  is 
going  on ;  that  is,  molecules  are  forming  or 
are  being  dissociated  into  atoms.  If  this  is  true 
in  all  cases,  the  Thomson  atom  also  accounts 
for  the  facts.  Chemical  action  consists  in  a 
rearrangement  of  corpuscles  to  form  attract- 
ing doublets,  or  in  the  passage  of  corpuscles 
from  one  atom  to  another ;  this  is  accompanied 
of  course  by  great  accelerations,  specially  at 
the  beginning  of  the  motion  of  transition  and 
at  the  end;  and  acceleration  of  a  corpuscle,  as 
we  have  seen,  is  a  requisite  for  the  emission 
of  radiant  energy.  Again,  the  whole  system  of 
corpuscles  in  any  molecule  will  have  a  certain 
average  acceleration  which  is  periodic,  and 


MODELS  OF  ATOMS  217 

different  molecular  groupings  of  the  same 
atoms  will  have  different  periodicities.  In  a 
previous  lecture  this  matter  has  been  discussed 
at  some  length;  and  the  important  facts 
brought  out  were  that  the  "  molecular  vibra- 
tions "  might  give  rise  to  the  isolated  lines  of 
a  discontinuous  spectrum ;  and  the  accelera- 
tions of  the  individual  corpuscles  as  they  leave 
and  join  atoms  would  cause  pulses  of  radiant 
energy  which  combine  to  form  a  continuous 
spectrum. 

The  conclusion  of  this  whole  discussion, 
then,  is  this :  If  we  assume  that  we  can  apply 
to  the  minute  structure  of  an  atom  the  gen- 
eral laws  of  dynamics  and  of  electricity  which 
our  experiments  on  material  bodies  and  on 
actual  charged  bodies  and  electric  currents 
lead  us  to  accept,  we  can  account  for  the  gen- 
eral phenomena  of  matter  by  considering  it 
made  up  of  atoms,  each  consisting  of  a  spheri- 
cal nucleus  of  positive  electrification  and 
groups  of  corpuscles.  This  hypothesis  has  the 
great  advantage  of  being  so  concrete  that  it 
has  suggested  and  will  continue  to  suggest 


218        THE  CONSTITUTION  OF  MATTER 

numerous  lines  of  experimental  investigation, 
all  leading  to  the  discovery  of  new  facts. 

When  we  come,  however,  to  a  more  careful 
consideration  of  the  phenomena  of  radiant 
energy,  that  is,  to  the  question  as  to  the  type 
of  disturbance  which  gives  rise  to  this  energy 
and  to  the  effect  produced  upon  matter  by  the 
reception  of  this  energy,  our  present  theory 
seems  to  fail.  This  points  to  the  possibility 
that  we  must  make  other  assumptions  in  re- 
gard to  the  connection  between  radiant  energy 
and  an  electric  charge.  Whatever  assumptions 
are  made  in  the  future,  they  must,  however, 
be  of  such  a  nature  as  to  leave  undisturbed 
the  facts  to  which  I  have  called  your  attention 
in  these  lectures.  We  may  obtain  a  new  series 
of  equations  for  dynamics  and  electricity ;  but 
they  cannot  differ  sufficiently  from  those  we 
have  used  to  lead  to  consequences  essentially 
different  from  those  which  follow  from  our 
present  equations,  when  these  are  tested  by 
the  observed  properties  of  ordinary  material 
bodies  or  by  ordinary  electric  phenomena.  In 
other  words,  a  continuous  increase  in  knowl- 


LAWS  OF  NATURE  219 

edge,  not  an  overthrow  of  past  achievements, 
is  to  be  expected. 

The  latter  half  of  this  lecture  I  wish  to  de- 
vote to  a  discussion  of  the  method  followed  in 
the  preceding  lectures,  and,  in  so  doing,  to 
describe  briefly  the  attitude  of  physicists  to- 
day towards  the  interpretation  of  natural  phe- 
nomena. As  was  said  in  the  first  lecture,  the 
general  line  of  progress  is:  first,  observation; 
second,  working  hypothesis;  third,  further  ex- 
perimental investigation.  The  value  of  a  good 
hypothesis  consists,  to  a  large  degree,  in  the 
stimulation  it  gives  to  new  experiments ;  for, 
whether  the  hypothesis  is  verified  or  not,  the 
facts  as  found  by  the  experiments  remain,  they 
are  permanent  and  of  ever-enduring  usefulness. 

Since  man  is  limited  in  the  formation  of 
mental  pictures  to  actual  experiences  or  to 
extensions  of  them,  and  since  his  attention  is 
first  called  to  physical  phenomena  by  his  senses, 
it  is  most  natural  that,  when  he  becomes  con- 
scious of  phenomena  to  which  his  senses  do 
not  respond,  he  should  attempt  to  devise  a 
mechanical  model,  i.e.,  a  material  mechanism 


220        THE  CONSTITUTION  OF  MATTER 

consisting  of  pulleys,  levers,  wheels,  cords,  etc., 
which  should  have  properties  as  nearly  as  pos- 
sible like  the  phenomena  concerned.  Lord 
Kelvin l  went  so  far  as  to  say  that  he  did  not 
understand  any  particular  point  in  physics 
unless  he  was  able  to  construct  a  mechanical 
model  of  it.  Thus,  in  studying  the  properties 
of  matter,  the  early  students  of  physics  pic- 
tured it  as  capable  of  subdivision  into  minute 
parts  called  molecules,  each  of  these  being 
essentially  like  the  whole  body.  Thus  un- 
doubtedly a  molecule  is  pictured  by  most 
people  as  a  minute  heavy  sphere.  Of  course, 
they  had  no  evidence  of  the  existence  of  a 
single  concrete  particle;  it  was  too  small  to 
see  or  to  weigh.  Many  phenomena  referring 
to  matter  had  been  observed;  some  of  these 
were  capable  of  mathematical  expression ;  what 
these  physicists  did  was  to  convince  themselves 
that,  if  there  were  minute  particles  of  matter 
endowed  with  certain  properties,  the  phenom- 
ena observed  with  actual  bodies  were  logical 
consequences  of  the  assumptions  made  with 

1  S.  P.  Thompson,  Life  of  Lord  Kelvin,  vol.  n,  p.  830. 


LAWS  OF  NATURE  221 

reference  to  the  molecules.  This  process  does 
not  constitute  a  proof  of  the  existence  of 
molecules.  In  order  to  demonstrate  this,  we 
must  first  prove  that  no  other  assumptions 
-will  lead  to  the  same  phenomena.  The  diffi- 
culty of  this  is  easily  understood.  Therefore, 
we  can  appreciate  the  point  of  view  of  a  phil- 
osopher who  says  that  he  does  not  care  to  go 
back  of  the  observed  phenomena  and  their 
statement  in  concise  laws,  but  prefers  to  stand 
upon  these  last  as  his  ultimate  knowledge.  As 
a  matter  of  fact,  Lord  Kelvin  had  moments 
of  uncertainty,  even  towards  the  end  of  his 
noble  career,  as  to  the  reality  of  molecules  as 
particles  of  matter.  Sir  J.  J.  Thomson  told 
me  that  once,  when  Kelvin  and  Stokes  were 
accompanying  him  through  his  laboratory, 
Kelvin  said  to  them  that  he  had  his  doubts 
about  the  molecular  nature  of  matter,  and 
Stokes  stopped  short  in  their  progress  and 
gave  what  Thomson  said  was  the  most  concise 
and  convincing  argument  in  regard  to  the 
molecular  constitution  of  matter  that  he  had 
ever  heard.  Kelvin  acknowledged  himself  fully 


222        THE  CONSTITUTION  OF  MATTER 

satisfied.  To  one  who  knew  the  two  men, 
Kelvin  and  Stokes,  the  greatest  men  of  their 
day  in  the  whole  realm  of  physical  science, 
the  incident  is  thoroughly  characteristic  of 
their  qualities.  As  a  matter  of  fact,  it  is 
doubtful  if  we  have  any  right  to  say  that  there 
ever  was  a  proof  of  the  existence  of  molecules, 
as  ordinarily  conceived,  until  the  experiments 
of  Rutherford  and  Geiger  upon  the  emission 
of  alpha  particles  by  radium,  to  which  refer- 
ence has  been  made  in  a  previous  lecture. 

Again,  consider  the  varied  phenomena 
which  we  associate  with  the  word  "  electric- 
ity." Clerk  Maxwell  succeeded  in  a  brilliant 
manner  in  expressing  by  a  series  of  beautiful 
equations  all  the  experimental  facts  discovered 
by  Faraday,  Cavendish,  and  the  long  line  of 
investigators.  His  concepts  were  two  kinds  of 
matter,  conductors  and  non-conductors,  each 
having  definite  electric  properties  to  which 
numbers  could  be  given,  and  a  universal  me- 
dium capable  of  transmitting  electric  and 
magnetic  forces,  called  the  a3ther.  The  equa- 
tions themselves  have  been  most  aptly  called 


LAWS  OF  NATURE  223 

"  Maxwell's  Theory  "  of  electricity ;  but  many 
eminent  scientists  were  not  content  until  they 
had  devised  mechanical  models,  which  gave 
motions  satisfying  mathematical  laws  identi- 
cal in  form  with  some  of  Maxwell's.  As  more 
electrical  phenomena  were  discovered,  notably 
the  Zeeman  effect,  it  was  necessary  to  modify 
Maxwell's  equations,  in  order  to  embrace  the 
new  facts;  and  this  was  most  satisfactorily 
done  by  H.  A.  Lorentz,  of  Leyden.  In  the 
interpretation  of  his  equations  Lorentz  used 
the  concepts  of  a  space  occupied  by  a  medium 
incapable  of  translation  and  of  a  number  of 
minute  electric  charges  called  "  electrons " 
which  are  distributed  through  this  medium. 
These  electrons  are  thought  of  as  being  in 
general  grouped  in  definite  geometrical  vol- 
umes, which  we  call  material  bodies;  and  the 
differences  between  conductors  and  non-con- 
ductors are  made  to  lie  in  the  mode  of  group- 
ing and  in  the  forces  acting  in  the  different 
groups.  (It  is  evident,  of  course,  that  the 
theory  is  not  based  entirely  upon  known  laws 
of  forces  between  charges,  but  assumes  the 


224        THE  CONSTITUTION  OF  MATTER 

existence  of  other  forces  not  yet  capable  of 
explanation.)  The  essential  difference  between 
Maxwell's  and  Lorentz's  theories  lies  in  the 
treatment  by  Maxwell  of  a  material  body,  such 
as  a  piece  of  glass,  as  a  body  by  itself,  having 
its  own  distinctive  properties ;  while  Lorentz 
considers  it  simply  as  a  geometrical  figure 
in  a  stationary  medium,  occupied  by  discrete 
electric  charges.  It  is  evident  that  Thomson's 
concept  of  an  atomic  negative  corpuscle  and 
an  equal  positive  charge  of  larger  volume  can 
be  at  once  introduced,  if  desired,  into  Lorentz's 
equations ;  so  of  course  can  many  other  con- 
cepts. The  equations  themselves  make  up 
what  we  may  call  our  definite  knowledge;  the 
interpretation  of  them  depends  upon  the  in- 
dividual point  of  view.  It  should  be  noted, 
however,  that,  although  both  Maxwell's  and 
Lorentz's  equations  are  stated  in  terms  of 
electric  and  magnetic  forces,  quantities  whose 
variations  can  be  noted  by  changes  in  bodies 
which  are  apparent  to  our  senses,  —  i.e.,  quan- 
tities which  may  be  measured  by  physical  in- 
struments, —  to  Maxwell  and  to  his  immediate 


LAWS  OF  NATURE  225 

followers  attention  was  concentrated  upon 
matter  as  such,  while  to  Lorentz  and  to  scien- 
tists to-day  all  thought  is  centred  upon  elec- 
tric charges.  Many  men  have  tried  and  many 
are  still  trying  to  picture  a  mechanism,  purely 
material  in  its  concept,  which  has  the  proper- 
ties of  an  electric  charge  ;  that  is,  they  attempt 
to  assign  such  mechanical  properties  as  mass, 
elasticity,  etc.,  to  a  medium  and  to  design  such 
models  as  will  exhibit  phenomena  capable  of 
expression  in  mathematical  laws  identical  with 
those  applicable  to  electric  charges.  At  the 
present  day,  however,  such  attempts  have  in 
the  main  ceased ;  and  most  people  are  content 
with  postulating  the  existence  of  electric 
charges  as  such.  This  does  not  mean  in  the 
least  that  this  is  to  be  the  final  stage  of  our 
interpretation  of  nature ;  the  whole  history  of 
the  development  of  science  is  absolutely  op- 
posed to  such  a  thought. 

As  a  further  illustration  of  the  main  idea 
which  I  am  trying  to  emphasize,  let  me  mention 
the  concept  of  radiant  energy,  which  I  have 
already  described  in  the  course  of  these  lectures. 


226        THE  CONSTITUTION  OF  MATTER 

It  was  a  direct  consequence  of  Maxwell's  equa- 
tions that  energy  emitted  into  the  aether  by 
oscillations  of  the  electric  and  magnetic  forces 
would  be  propagated  with  a  definite  velocity 
which  was  identified  with  the  so-called  "velocity 
of  light."  The  same  is  true,  of  course,  of  Lor- 
entz's  equations,  which  are  simply  extensions  of 
Maxwell's.  To  Maxwell,  however,  this  oscilla- 
tion of  the  electric  and  magnetic  forces  was  due 
primarily  to  a  motion  of  a  charge  on  the  surface 
of  a  conductor  or  to  the  variation  of  a  current  in 
a  conductor,  i.e.,  the  electric  charge  and  the 
current  were  treated  separately.  Lorentz,  on 
the  other  hand,  thinks  of  a  real  acceleration 
in  space  of  an  electrical  charge  as  being  the 
cause  of  the  radiation. 

The  mechanism  of  the  propagation  does  not 
enter  into  either  theory.  Before  anything  could 
be  said  on  the  subject,  it  would  be  necessary  to 
describe  the  properties  of  the  aether  in  terms  of 
the  characteristics  of  matter.  Thomson  showed 
mathematically,  however,  many  years  ago  that 
it  was  possible  to  picture  the  process  of  radia- 
tion as  the  advance  through  the  aether  of  tubes 


LAWS  OF  NATURE  227 

of  electric  force.  These  are  drawn  differently 
from  the  ones  of  which  I  have  spoken  in  the 
preceding  lectures.  According  to  the  view 
adopted  by  Thomson  within  recent  years, 
each  corpuscle  has  permanently  attached  to  it 
certain  radial  tubes;  in  the  older,  classical 
method,  a  line  of  force  at  any  point  of  space 
has  the  direction  of  the  resultant  force  at  that 
point  due  to  all  the  charges  acting,  positive  and 
negative ;  so  there  is  an  imaginary  geometrical 
line  of  force  at  every  point  of  the  electric  field. 
In  general,  of  course,  as  there  are  always  equal 
amounts  of  positive  and  negative  charges,  lines 
of  force  will  always  begin  on  one  and  end  on  the 
other.  But  Thomson  and  also  Hertz  showed 
that  in  the  case  of  electric  oscillations,  —  such 
as  are  used,  for  instance,  in  wireless  telegraphy, 
—  tubes  of  force,  as  thus  defined,  exist  in  the 
aether,  forming  closed  curves,  and  that  these 
tubes  travel  with  the  velocity  of  light.  By  at- 
tributing a  real  existence  to  these  moving  tubes, 
Thomson  explained  in  an  exceedingly  simple 
manner  many  of  the  phenomena  of  electricity 
and  light. 


228         THE  CONSTITUTION  OF  MATTER 

Maxwell's  equations  and  theory  say  nothing 
explicitly  in  regard  to  the  way  radiation  is  pro- 
duced ;  Lorentz,  on  the  other  hand,  predicates 
an  electron  having  an  acceleration.  In  this  last 
case,  the  electron  will  carry  with  it  in  its  mo- 
tion its  electric  field ;  but  outside  this,  at  a  dis- 
tance from  the  electron  which  is  large  com- 
pared with  its  dimensions,  there  will  be  a 
"radiation  field/'  consisting  of  outspreading 
spherical  waves.  In  neither  theory  is  there 
any  condition  making  it  necessary  for  the 
wave-front  to  be  continuous ;  both  theories  state 
that  at  any  point  in  the  aether  where  the  elec- 
tric force  has  a  value  the  conditions  are  such 
as  correspond  to  the  advance  along  a  certain 
line  of  the  disturbance  existing  there.  The 
geometrical  surface  perpendicular  to  these  lines 
we  may  call  the  wave-front.  However,  there  is 
no  reason  on  either  of  the  two  theories  why- 
the  electric  force  should  not  have  a  value  at 
all  points  of  space,  which  would,  therefore, 
require  a  continuous  wave-front. 

Thomson  was  the  first,  as  has  been  said,  to 
advance  the  idea  that  an  electric  charge  does 


LAWS   OF  NATURE  229 

not  produce  a  continuous  field  of  force;  and 
his  scheme  for  securing  such  a  condition  is  to 
make  the  hypothesis  that  a  corpuscle  possesses 
a  limited  number  of  permanently  attached  ra- 
dial tubes  which  are  capable  of  propagating  a 
transverse  disturbance.  This  is  an  addition  to 
Lorentz's  theory,  inasmuch  as  the  action  of 
the  electric  force  is  limited  to  certain  lines; 
i.e.,  at  all  points  off  these  lines  we  must  equate 
the  force  to  zero.  With  this  modification,  we 
may  apply  Lorentz's  equations  and  draw  all 
the  conclusions  which  he  and  others  have  done. 
Within  a  very  recent  time  a  distinctly  new 
idea  has  been  brought  forward  by  Planck  in 
the  treatment  of  the  emission  of  radiant  energy. 
We  have  seen  that  the  three  fundamental  ele- 
mentary entities  in  terms  of  which  we  aim  to 
explain  physical  nature  are  corpuscles,  atoms, 
and  energy.  We  can  reduce  the  consideration 
of  all  charges  and  all  matter  to  ultimate  parts; 
all  corpuscles  are  alike ;  the  atoms  of  any  one 
element  are  identically  alike  so  far  as  there 
is  any  evidence.  Planck  suggested  that,  in 
a  similar  manner,  radiant  energy  consists  of 


230         THE  CONSTITUTION  OF  MATTER 

ultimate  parts,  those  emitted  by  any  one  type 
of  atom  being  identically  alike.  This  is  a  most 
startling  suggestion  at  first  sight,  and  was  not 
at  first  received  with  great  favor,  although,  as 
Thomson  has  shown,  it  is  a  consequence  of 
the  fact  that  a  definite  amount  of  energy  is 
required  to  drive  a  corpuscle  out  of  any  mole- 
cule. 

In  Planck's  theory,  the  source  of  radiation 
is  a  definite  type  of  electric  oscillator ;  and  by 
making  certain  assumptions,  concerning  the 
plausibility  and  meaning  of  which  there  has 
been  considerable  dispute,  he  arrives  at  the 
conclusion  that  there  is  an  elementary  quan- 
tity or  "  quantum  "  of  radiant  energy,  char- 
acteristic of  each  oscillator,  or  "  radiator,"  as 
he  prefers  to  call  it.  Thus  each  radiator  emits 
only  whole  numbers  of  these  quanta.  How- 
ever, when  such  a  radiator  absorbs  energy, -it 
does  so  by  a  continuous  process.  The  numer- 
ous difficulties  in  Planck's  theory  have  been 
well  brought  out  by  Professor  Wien,  of  the 
University  of  Wiirtzburg,  in  his  article  on 
"  Theory  of  Radiation  "  in  the  "  Encyclopedia 


LAWS  OF  NATURE  231 

of  the  Mathematical  Sciences." 1  Planck  was 
able,  however,  by  his  assumptions  to  deduce 
a  formula  which  expresses  in  a  most  satisfac- 
tory manner  the  facts  of  the  radiation  by 
"  black  bodies,"  and  also,  by  comparing  his 
formulae  with  known  facts,  to  deduce  values 
for  the  elementary  atomic  charge,  the  number 
of  molecules  in  a  given  volume  of  a  gas,  etc., 
all  of  which  agree  well  with  those  obtained 
by  more  direct  means.2 

Taking  Newton's  equations  as  typical  of 
our  theories  of  mechanics  and  Maxwell's  as 
typical  of  our  electrical  theories,  it  is  impor- 
tant to  realize  that  the  test  of  their  usefulness 
primarily  is  their  statement  of  the  facts  of 
nature  as  we  observe  them.  We  are  living  on 
the  earth,  a  body  each  point  of  which  is  mov- 
ing rapidly  in  space ;  further,  our  instruments 

1  See   also   Poincare*,  Journal  de  Physique   (v),  vol.   n, 
pp.  5,  347  (1912). 

2  For  an  interesting  description  of  the  "  quantum  "  theo- 
ries of  radiation,  see  an  article  by  Millikan  in  Science,  Janu- 
ary, 1913.  There  is  an  intimate  connection  between  this  hy- 
pothesis of  Planck  and  the  general  theory  of  equipartition  of 
energy  in  all  forms,  as  is  shown  by  recent  work  on  specific 
heats. 


232        THE  CONSTITUTION  OF  MATTER 

allow  us  to  measure  only  those  quantities 
which  are  of  limited  dimensions.  What  equa- 
tions would  hold  if  the  earth  were  at  rest  in 
space,  granting  that  the  idea  is  conceivable, 
or  what  are  the  properties  of  extremely  minute 
quantities  or  very  large  ones,  or  of  bodies 
moving  with  great  velocities,  etc.,  we  have  no 
way  of  knowing.  We  can  assume,  of  course, 
that  the  equations  which  we  have  apply  to 
quantities  of  all  dimensions,  large  and  small ; 
and  we  can  use  ordinary  mathematical  proc- 
esses to  extend  our  equations  to  the  relative 
motion  of  bodies  with  reference  to  a  frame  of 
reference  fixed  in  space.  This  is,  as  a  matter 
of  fact,  what  has  been  done  by  Lorentz,  Thom- 
son, and  others ;  and  the  results  of  this  method 
are  those  which  I  have  given  in  these  lectures. 
Even  in  the  adoption  of  this  procedure  certain 
modifications  have  to  be  made  in  Newton's 
laws  of  motion.  In  these  laws  Newton  in- 
cluded only  the  mass  of  material  bodies ;  but, 
by  the  application  of  Maxwell's  equations,  it 
soon  became  evident  that  radiant  energy  also 
possessed  mass,  and  so  Newton's  laws  as  origi- 


LAWS  OF  NATURE  233 

nally  stated  are  not  in  accord  with  facts. 
Thus,  a  source  of  light  owing  to  its  radiation 
experiences  a  reaction;  and  when  the  radia- 
tion falls  upon  any  body  it  is  pushed  in  the 
direction  of  the  beam  of  light.  Of  course,  this 
effect  is  extremely  minute  and  requires  special 
apparatus  for  its  detection.  Again,  difficulties 
enter  when  we  attempt  to  define  what  is  meant 
by  equal  intervals  of  time  or  by  equal  lengths 
or  by  saying  that  two  events  on  different  bod- 
ies, e.g.,  the  sun  and  the  earth,  occur  simul- 
taneously. 

Our  only  justification  in  the  method  we 
have  followed  in  using  and  extending  our 
equations  comes  from  the  fact  that  the  conse- 
quences deduced  have  been  reasonable  and 
consistent  with  each  other.  We  must  also  bear 
in  mind  that  we  might  equally  well  have 
adopted  equations  which  differed  extremely 
little  from  our  accepted  ones ;  and  we  would 
have  no  way  of  deciding  between  the  two  if 
we  applied  them  to  ordinary  phenomena.  If 
by  the  extension  of  our  fundamental  equations 
we  are  led  to  any  deduction  which  is  contrary 


234        THE  CONSTITUTION  OF  MATTER 

to  fact,  it  shows  that  our  hypotheses  are 
wrong ;  if  we  are  led  to  deductions  which  seem 
improbable,  —  a  very  dubious  expression,  — 
we  might  be  tempted  to  make  an  entirely  new 
start,  make  new  hypotheses,  and  develop  a 
new  mathematical  analysis.  This  condition  has 
arisen.  In  speaking  of  the  rapid  motion  of 
material  bodies  through  space,  I  called  your 
attention  to  the  fact  that  a  logical  consequence 
of  Lorentz's  theory  is  the  change  of  dimen- 
sions of  the  moving  body,  a  eontraction  in  the 
line  of  motion.  This  seemed  to  some  people 
to  be  a  conclusion  which  was  what  I  may  call 
artificial ;  and  in  any  case  the  equations  de- 
veloped by  Lorentz  to  apply  to  rapidly  moving 
bodies  were  of  extraordinary  complexity. 

As  a  consequence  of  these  and  other 
facts,  Professor  Einstein,  of  the  University  of 
Prague,  has  developed  an  entirely  new  philos- 
ophy of  natural  phenomena.  He  begins  by 
making  several  fundamental  assumptions,  one 
of  which  is  that  all  phenomena  are  electrical 
in  their  origin,  and  draws  the  consequences 
by  rigid  mathematical  steps.  The  hypotheses 


LAWS  OF  NATURE  235 

which  he  makes  are  not  sufficient  to  permit 
the  deduction  of  all  the  equations  we  need  for 
a  complete  theory  of  nature ;  but,  so  far  as  the 
development  has  been  carried,  the  results  are 
most  satisfactory.  It  may  be  of  interest  to 
note  a  few  of  the  statements  of  the  theory; 
there  is  no  universal  medium  such  as  a  station- 
ary aBther ;  the  idea  of  giving  a  number  to  a 
length  is  a  matter  of  definition ;  whenever  the 
velocity  of  light  enters  into  an  equation,  it 
has  the  properties  of  a  number  infinitely  large, 
that  is,  adding  to  it  or  subtracting  from  it  a 
finite  number  leaves  it  unaltered ;  if  one  body 
is  moving  with  reference  to  another  with  a 
velocity  Vi,  and  the  second  is  moving  with 
reference  to  a  third  with  a  velocity  V2,  the 
velocity  of  the  first  with  reference  to  the  third 
is  not  the  sum  of  Vi  and  v2,  as  it  is  in  the 
ordinary  mechanics  of  Newton  (but  the  re- 
sults are  the  same,  provided  the  two  numbers 
are  small).  Einstein's  point  of  view  towards 
nature  is  more  that  of  what  is  called  a  philos- 
opher than  of  an  investigator.  His  hypothe- 
ses are  not  suggested  directly  by  our  sense- 


236        THE  CONSTITUTION  OF  MATTER 

experiences,  but  are  statements  which  seem 
reasonable;  but  their  sole  justification,  from 
a  physical  sense,  will  rest  in  their  deductions 
being  in  accord  with  observations.  In  New- 
ton's and  Maxwell's  hypotheses,  the  experi- 
mental observations  came  first,  and  directly 
suggested  the  mathematical  assumptions.  The 
conclusion  drawn  by  Jeans  and  others  from  the 
recent  experimental  work  on  radiant  energy 
and  specific  heats  of  solid  bodies  is  that  the 
facts  of  nature  cannot  be  deduced  from  differ- 
ential equations  — which  assume  continuity  in 
space  and  time. 

That  modern  science  is  built  on  a  sure  foun- 
dation no  one  can  doubt ;  from  the  publication 
of  Newton's  "  Principia  "  to  the  present  day, 
the  progress  has  been  continuous.  Each  year 
our  vision  is  broader,  and  the  explanation  lies 
in  the  fact  that  our  understanding  of  the  mi- 
nute phenomena  of  nature  is  clearer.  No  one 
conception  has  been  so  inspiring  and  so  sug- 
gestive as  that  of  Thomson  as  to  the  corpus- 
cular structure  of  matter ;  and  no  mathemati- 
cal discussion  has  been  so  luminous  as  that  of 


CONCLUSION  237 

Lorentz  of  the  properties  of  corpuscles  or 
electrons.  Whatever  wealth  of  knowledge  the 
future  has  in  store  for  us  relating  to  the  con- 
nection between  corpuscles,  atoms,  and  en- 
ergy, no  names  will  stand  out  more  clearly  in 
the  history  of  thought  in  the  twentieth  cen- 
tury than  those  of  Joseph  John  Thomson  and 
Heindrik  Antoon  Lorentz. 


THE   END 


INDEX 


ABSORPTION  of  radiation,  144, 
193. 

Actinium,  transformations  of, 
95. 

.(Ether,  the,  27;  aether,  bound, 
70,  143. 

Alpha  particles,  85,  92. 

Ampere;  theory  of  magnetism, 
199. 

Atom,  mass  of,  explanation  of, 
74;  models  of,  200. 

Atom  of  matter,  37;  of  elec- 
tricity, 48. 

Atomic  weights,  40. 

Becquerel,  Henri;  discovery  of 

radio-activity,  91. 
Bessel;  pendulum  experiments, 

119. 

Beta  particles,  65,  92. 
Black  body  radiation,  133. 
Brown,  E.  W.;  motion  of  the 

moon,  105. 
Bucherer;  experiments  on  beta 

particles,  65. 

Canal  rays,  47. 

Cathode  rays,  44. 

Chemical     combination.     See 

Molecules,  formation  of. 
Comstock,    D.    F.;    electrical 

mass,  69. 
Conductivity    for    electricity, 

176,  185;  for  heat,  176,  184. 


Conductors    and   non-conduc- 
tors, 53,  169,  183. 
Corpuscles,   mass  of,   44,   63; 

number   of,    in   atoms,   75; 

charge  of,  80,  87;  size  of,  88; 

shape  of,  88;  radiation  from, 

134  et  seq. 
Corpuscular  theory  of  metals, 

183. 
Crowther,  J.  R.;  distribution 

of  positive  charge  in  atoms, 

214. 
Curie,  Madame;  radio-activity, 

91. 

Discontinuous  spectra,  132. 
Doublets,  electric,  76, 156,  161. 

216. 
Drude;  theory  of  metals,  183. 

•jj  for  a  corpuscle,  83. 

Einstein;  principle  of   relativ- 
ity, 168,  234. 
Elasticity,  11,  26,  161. 
Electric  charge,  mass  of,  63. 
Electric  currents,  58,  176,  185. 
Electrification,  53. 
Electrokinetic  energy,  59. 
Electron.     See  Corpuscles. 
Electro-positive  atoms,  160. 
Electrostatic  energy,  57. 
Elements,  chemical,  37. 
Energy,   30;  conservation  of, 


240 


INDEX 


32,  86;  radiant  (see  Radia- 
tion); of  electrification,  35; 
of  electric  currents,  35. 

Equilibrium,  statistical,  150, 
171,  183. 

Ether.     See  .Ether. 

Faraday,  56,  143,  177. 
Fitzgerald;  deformation  of  mov- 
ing bodies,  166. 
Fluorescence,  147. 
Force,  definition  of,  23. 
Force,  lines  of,  70,  142,  227. 
Forces,  molecular,  164. 
Free  corpuscles  in  metals,  183. 

Galileo;  experiments  on  im- 
pact, 21,  128;  general  con- 
cepts of  matter,  22,  128;  ex- 
periments with  falling  bodies, 
107;  experiments  with  pend- 
ulums, 109. 

Gamma  rays,  92. 

Geiger;  counting  of  alpha  par- 
ticles, 85. 

Goldstein;  canal  rays,  47. 

Gravitation;  Newton's  Law, 
99;  explanation  of,  124;  and 

.    radio-activity,  121. 

Gray  and  Ramsay;  atomic 
weight  of  radium  emanation, 
94. 

Ilasenohrl;  mass  of  radiation, 

69. 
Heaviside,  O.;  distribution  of 

lines  of  force,  72. 
Helium,    formed    from    alpha 

particles,  85. 
Hydrogen  atom,  mass  of,  81. 


Impact,  12. 

Inertia,  10.     See  Mass, 
lonization  in  gases,  46;  in  solu- 
tions, 149. 
Ions,  149. 

Jeans,  J.  H.;  partition  of  en- 
ergy, 236. 

Kaufmann;  mass  of  a  beta  par- 
ticle, 65. 

Kayser  and  Runge;  spectrum 
series,  137. 

Kelvin,  Lord,  121,  181,  220, 
221. 

Kepler's  laws,  103. 

Kinetic  energy,  30,  180. 

Kinetic  theory  of  matter,  38. 

Langevin;  theory  of  magne- 
tism, 199. 

Larmor,  J.;  radiation,   134. 

LeSage;  theory  of  gravitation, 
127. 

Lorentz,  H.  A.;  shape  of  a  cor- 
puscle, 88;  explanation  of 
gravitation,  126;  production 
of  radiation,  134;  deforma- 
tion of  moving  bodies,  166; 
theory  of  electrons,  223. 

MacKenzie,  A.  S.;  experiments 
upon  gravitation,  120. 

Magnetism,  197. 

Magneton,  198. 

Mass,  definition  of,  16;  conser- 
vation of,  18;  of  electric 
charge,  63;  described  in  terms 
of  potential  energy,  67;  of 
radiation,  68;  explanation  of, 
63  et  seq. 


INDEX 


241 


Matter,  general  discussion  of 
4;  kinetic  theory  of,  38. 

Maxwell;  electric  waves,  61, 
226;  theory  of  electricity, 
222. 

Mendel£eff's  periodic  table 
41. 

Metals,  properties  of,  183;  re- 
flection from,  195. 

Michelson  and  Morley;  ex- 
periments upon  matter  and 
sether,  166. 

Millikan;  experiments  upon 
corpuscles,  79. 

Molecules,  37;  number  of  mole- 
cules per  cubic  centimeter, 
39,  82;  formation  of,  149. 

Momentum,  19. 

Muscle  sense,  9. 

Nagaoka,  model  of  an  atom, 
214. 

Newcomb,  Simon;  law  of  grav- 
itation, 106. 

Newton;  experiments  on  im- 
pact, 13;  idea  of  mass,  16; 
of  force,  23;  laws  of  motion, 
22;  law  of  gravitation,  99; 
experiments  with  pendu- 
lums, 118. 

Periodic  system  of  the  elements, 

41. 
Perrin;    Brownian  movement, 

39. 
Pfund,    A.    H.;    properties   of 

selenium,  192. 
Phosphorescence,  147. 
Photo-electric  effect,  190. 
Planck;    theory    of   radiation, 

134,  229. 


Positive  charge  of  electricity, 

54,  60. 
Potential  energy,  30;  mass  due 

to,  67. 

Radiation,  34,  130 ;  produc- 
tion of,  61,  132;  propagation 
of,  61,  142,  226;  velocity  of, 
62;  mass  of,  68;  absorption 
of,  145,  192. 

Radio-active  transformations, 
95. 

Radio-activity,  46,  49,  90. 

Radium,  etc.  (See  Radio-activ- 
ity); transformations  of,  95. 

Reflection  of  light,  195. 

Richardson,  O.  W.;  thermion- 
ics,  187. 

Roentgen  rays,  42,  90. 

Rutherford,  E.;  model  of  an 
atom,  214;  experiments  in 
radio-activity,  85. 

Rydberg ;  relations  between 
atomic  weights,  43. 

Scientific  method,  the,  8. 
Selenium,  192. 

Southerns,     L.;     experiments 
upon  weight  and  mass,  123. 
Spectroscopy,  42,  131. 

Temperature  and  kinetic  en- 
ergy of  molecules  or  cor- 
puscles, 180. 

Temperature  sense,  8. 

Thermions,  187. 

Thermometric  scales,  179. 

Thomson,  J.  J.;  properties  of 
corpuscles,  43;  of  canal  rays, 
47;  concept  of  electrical 
mass,  64;  concept  of  tubes 


INDEX 


of  force,  70, 142;  of  radiation, 
139,  143,  227;  experiments 
upon  weight  and  mass,  123; 
model  of  an  atom,  201. 

Thorium,  transformations  of, 
96. 

Townsend,  charge  of  corpuscles, 
81. 

Uranium,  transformations  of, 
95. 

Valency,  156,  206. 
Viscosity,  162. 


Weight,  10,  25,  99. 

Weight  of  radio-active  bodies, 
121. 

Weiss,  P.;  theory  of  magne- 
tism, 198. 

Wilson,  C.  T.  R.;  photographs 
of  ionization,  141. 

Wilson,  H.  A.;  experiments  on 
corpuscles,  81;  model  of  an 
atom,  214. 

Wood,  R.  W.;  experiments  on 
fluorescence,  148. 

Work,  definition  of,  29. 

Zeeman  effect,  46. 


CAMBRIDGE  .  MASSACHUSETTS 
U   .   S    .   A 


THIS  BO.K  IS 

STAMPED  BELOW 


MAR  30  1915 

. 

a 


i921 

JUN  U1959 


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SITY  OF  'CALIFORNIA  LIBRARY 


